Butzer, Paul Leo 1928
Overview
Works:  257 works in 746 publications in 7 languages and 6,163 library holdings 

Genres:  Conference papers and proceedings History 
Roles:  Author, Editor, Honoree, Other, Creator, Contributor, Thesis advisor 
Publication Timeline
.
Most widely held works by
Paul Leo Butzer
Fourier analysis and approximation by
Paul Leo Butzer(
Book
)
49 editions published in 1971 in 3 languages and held by 645 WorldCat member libraries worldwide
At the international conference on 'Harmonic Analysis and Integral Transforms', conducted by one of the authors at the Mathematical Research Institute in Oberwolfach (Black Forest) in August 1965, it was felt that there was a real need for a book on Fourier analysis stressing (i) parallel treatment of Fourier series and Fourier trans forms from a transform point of view, (ii) treatment of Fourier transforms in LP(lRn)_ space not only for p = 1 and p = 2, (iii) classical solution of partial differential equations with completely rigorous proofs, (iv) theory of singular integrals of convolu tion type, (v) applications to approximation theory including saturation theory, (vi) multiplier theory, (vii) Hilbert transforms, Riesz fractional integrals, Bessel potentials, (viii) Fourier transform methods on locally compact groups. This study aims to consider these aspects, presenting a systematic treatment of Fourier analysis on the circle as well as on the infinite line, and of those areas of approximation theory which are in some way or other related thereto. A second volume is in preparation which goes beyond the onedimensional theory presented here to cover the subject for functions of several variables. Approximately a half of this first volume deals with the theories of Fourier series and of Fourier integrals from a transform point of view
49 editions published in 1971 in 3 languages and held by 645 WorldCat member libraries worldwide
At the international conference on 'Harmonic Analysis and Integral Transforms', conducted by one of the authors at the Mathematical Research Institute in Oberwolfach (Black Forest) in August 1965, it was felt that there was a real need for a book on Fourier analysis stressing (i) parallel treatment of Fourier series and Fourier trans forms from a transform point of view, (ii) treatment of Fourier transforms in LP(lRn)_ space not only for p = 1 and p = 2, (iii) classical solution of partial differential equations with completely rigorous proofs, (iv) theory of singular integrals of convolu tion type, (v) applications to approximation theory including saturation theory, (vi) multiplier theory, (vii) Hilbert transforms, Riesz fractional integrals, Bessel potentials, (viii) Fourier transform methods on locally compact groups. This study aims to consider these aspects, presenting a systematic treatment of Fourier analysis on the circle as well as on the infinite line, and of those areas of approximation theory which are in some way or other related thereto. A second volume is in preparation which goes beyond the onedimensional theory presented here to cover the subject for functions of several variables. Approximately a half of this first volume deals with the theories of Fourier series and of Fourier integrals from a transform point of view
Semigroups of operators and approximation by
Paul Leo Butzer(
Book
)
28 editions published in 1967 in English and German and held by 583 WorldCat member libraries worldwide
In recent years important progress has been made in the study of semigroups of operators from the viewpoint of approximation theory. These advances have primarily been achieved by introducing the theory of intermediate spaces. The applications of the theory not only permit integration of a series of diverse questions from many domains of mathematical analysis but also lead to significant new results on classical approximation theory, on the initial and boundary behavior of solutions of partial differential equations, and on the theory of singular integrals. The aim of this book is to present a systematic treatment of semi groups of bounded linear operators on Banach spaces and their connec tions with approximation theoretical questions in a more classical setting as well as within the setting of the theory of intermediate spaces. However, no attempt is made to present an exhaustive account of the theory of semigroups of operators per se, which is the central theme of the monumental treatise by HILLE and PHILLIPS (1957). Neither has it been attempted to give an account of the theory of approximation as such. A number of excellent books on various aspects of the latter theory has appeared in recent years, so for example CHENEY (1966), DAVIS (1963), LORENTZ (1966), MEINARDUS (1964), RICE (1964), SARD (1963). By contrast, the present book is primarily concerned with those aspects of semigroup theory that are connected in some way or other with approximation
28 editions published in 1967 in English and German and held by 583 WorldCat member libraries worldwide
In recent years important progress has been made in the study of semigroups of operators from the viewpoint of approximation theory. These advances have primarily been achieved by introducing the theory of intermediate spaces. The applications of the theory not only permit integration of a series of diverse questions from many domains of mathematical analysis but also lead to significant new results on classical approximation theory, on the initial and boundary behavior of solutions of partial differential equations, and on the theory of singular integrals. The aim of this book is to present a systematic treatment of semi groups of bounded linear operators on Banach spaces and their connec tions with approximation theoretical questions in a more classical setting as well as within the setting of the theory of intermediate spaces. However, no attempt is made to present an exhaustive account of the theory of semigroups of operators per se, which is the central theme of the monumental treatise by HILLE and PHILLIPS (1957). Neither has it been attempted to give an account of the theory of approximation as such. A number of excellent books on various aspects of the latter theory has appeared in recent years, so for example CHENEY (1966), DAVIS (1963), LORENTZ (1966), MEINARDUS (1964), RICE (1964), SARD (1963). By contrast, the present book is primarily concerned with those aspects of semigroup theory that are connected in some way or other with approximation
Linear operators and approximation. Proceedings of the Conference held at the Oberwolfach Mathematical Research Institute,
Black Forest, August 1422, 1971 by
Paul Leo Butzer(
Book
)
59 editions published between 1972 and 1974 in 4 languages and held by 518 WorldCat member libraries worldwide
These proceedings contain the lectures presented at the Conference on Linear Operators and Approximation held at the Oberwolfach Mathematical Research In stitute, August 1422, 1971. There were thirtyeight such lectures while four addi tional papers, subsequently submitted in writing, are also included in this volume. Two of the three lectures presented by Russian mathematicians are rendered in English, the third in Russian. Furthermore, there is areport on new and unsolved problems based upon special problem sessions, with later communications from the participants. In fact, two of the papers inc1uded are devoted to solutions of some of the problems posed. The papers have been classified according to subject matter into five chapters, but it needs little emphasis that such thematic groupings are necessarily somewhat arbitrary. Thus Chapter I on Operator Theory is concerned with linear and non linear semigroups, structure of single operators, unitary operators, spectral and ergodic theory. Chapter Il on Topics in Functional Analysis inc1udes papers on Riesz spaces, boundedness theorems, generalized limits, and distributions. Chapter III, entitled "Approximation in Abstract Spaces", ranges from characterizations of c1asses of functions in approximation theory to approximationtheoretical topics connected with extensions to Banach (or more general) spaces. Chapter IV contains papers on harmonic analysis in connection with approximation and, finally, Chapter V is devoted to approximation by splines, algebraic polynomials, rational functions, and to Pade approximation. A large part of the general editorial work connected with these proceedings was competently handled by Miss F. Feber, while G
59 editions published between 1972 and 1974 in 4 languages and held by 518 WorldCat member libraries worldwide
These proceedings contain the lectures presented at the Conference on Linear Operators and Approximation held at the Oberwolfach Mathematical Research In stitute, August 1422, 1971. There were thirtyeight such lectures while four addi tional papers, subsequently submitted in writing, are also included in this volume. Two of the three lectures presented by Russian mathematicians are rendered in English, the third in Russian. Furthermore, there is areport on new and unsolved problems based upon special problem sessions, with later communications from the participants. In fact, two of the papers inc1uded are devoted to solutions of some of the problems posed. The papers have been classified according to subject matter into five chapters, but it needs little emphasis that such thematic groupings are necessarily somewhat arbitrary. Thus Chapter I on Operator Theory is concerned with linear and non linear semigroups, structure of single operators, unitary operators, spectral and ergodic theory. Chapter Il on Topics in Functional Analysis inc1udes papers on Riesz spaces, boundedness theorems, generalized limits, and distributions. Chapter III, entitled "Approximation in Abstract Spaces", ranges from characterizations of c1asses of functions in approximation theory to approximationtheoretical topics connected with extensions to Banach (or more general) spaces. Chapter IV contains papers on harmonic analysis in connection with approximation and, finally, Chapter V is devoted to approximation by splines, algebraic polynomials, rational functions, and to Pade approximation. A large part of the general editorial work connected with these proceedings was competently handled by Miss F. Feber, while G
On approximation theory : proceedings of the conference held in the Mathematical Research Institute at Oberwolfach, Black
Forest, August 410, 1963 = Über Approximationstheorie : Abhandlungen zur Tagung im Mathematischen Forschungsinstitut Oberwolfach,
Schwarzwald, vom 4.10. August 1963 by
Paul Leo Butzer(
Book
)
65 editions published between 1964 and 1972 in 5 languages and held by 373 WorldCat member libraries worldwide
65 editions published between 1964 and 1972 in 5 languages and held by 373 WorldCat member libraries worldwide
Abstract spaces and approximation. Abstrakte Räume und Approximation. Proceedings of the conference held at the Mathematical
Research Institute at Oberwolfach, Black Forest, July 1827, 1968 by
Paul Leo Butzer(
Book
)
42 editions published between 1968 and 1969 in 3 languages and held by 341 WorldCat member libraries worldwide
The present conference took place at Oberwolfach, July 1827, 1968, as a direct followup on a meeting on Approximation Theory [1] held there from August 410, 1963. The emphasis was on theoretical aspects of approximation, rather than the numerical side. Particular importance was placed on the related fields of functional analysis and operator theory. Thirtynine papers were presented at the conference and one more was subsequently submitted in writing. All of these are included in these proceedings. In addition there is areport on new and unsolved problems based upon a special problem session and later communications from the partici pants. A special role is played by the survey papers also presented in full. They cover a broad range of topics, including invariant subspaces, scattering theory, WienerHopf equations, interpolation theorems, contraction operators, approximation in Banach spaces, etc. The papers have been classified according to subject matter into five chapters, but it needs little emphasis that such thematic groupings are necessarily arbitrary to some extent. The Proceedings are dedicated to the memory of Jean Favard. It was Favard who gave the Oberwolfach Conference of 1963 a special impetus and whose absence was deeply regretted this time. An appreciation of his li fe and contributions was presented verbally by Georges Alexits, while the written version bears the signa tures of both Alexits and Marc Zamansky. Our particular thanks are due to E
42 editions published between 1968 and 1969 in 3 languages and held by 341 WorldCat member libraries worldwide
The present conference took place at Oberwolfach, July 1827, 1968, as a direct followup on a meeting on Approximation Theory [1] held there from August 410, 1963. The emphasis was on theoretical aspects of approximation, rather than the numerical side. Particular importance was placed on the related fields of functional analysis and operator theory. Thirtynine papers were presented at the conference and one more was subsequently submitted in writing. All of these are included in these proceedings. In addition there is areport on new and unsolved problems based upon a special problem session and later communications from the partici pants. A special role is played by the survey papers also presented in full. They cover a broad range of topics, including invariant subspaces, scattering theory, WienerHopf equations, interpolation theorems, contraction operators, approximation in Banach spaces, etc. The papers have been classified according to subject matter into five chapters, but it needs little emphasis that such thematic groupings are necessarily arbitrary to some extent. The Proceedings are dedicated to the memory of Jean Favard. It was Favard who gave the Oberwolfach Conference of 1963 a special impetus and whose absence was deeply regretted this time. An appreciation of his li fe and contributions was presented verbally by Georges Alexits, while the written version bears the signa tures of both Alexits and Marc Zamansky. Our particular thanks are due to E
E.B. Christoffel, the influence of his work on mathematics and the physical sciences by
Paul Leo Butzer(
Book
)
23 editions published in 1981 in 4 languages and held by 310 WorldCat member libraries worldwide
This memorial volume is dedicated to E.B. Christoffel on the occasion of the 150th anniversary of his birth. Its aim is, on the one hand, to present the life of Christoffel and the scientific milieu in which he worked and, on the other hand, to present a survey of his work not only in its historical context but especially in the frame of contemporary mathematics and physics. For one thing, this book contains expanded versions of the twelve invited lectures given at the International Christoffel Symposium, held on November 8 11, 1979 at Aachen and Monschau. For another, the scope of these papers has been broadened by soliciting some fourtyfive additional invited articles, concerned either with further aspects of the work of Christoffel or with specia lized topics in fields in which Christoffel had worked. This should give the reader a greater opportunity to appreciate the richness of Christoffel's contributions to the mathematical and physical sciences, and not only its immediate impact but also its subsequent infiuence. It can be discerned that Christoffel did basic work not only in differential geometry or, better still, in classical tensor analysis, thereby supplying the mathematical foundations of Einstein's theory of general relativity, but also in a variety of other areas of mathematics. The scope of Christoffel's work can be appreciated from the following synopsis of the thirteen chapters into which the festschrift is divided. Chap
23 editions published in 1981 in 4 languages and held by 310 WorldCat member libraries worldwide
This memorial volume is dedicated to E.B. Christoffel on the occasion of the 150th anniversary of his birth. Its aim is, on the one hand, to present the life of Christoffel and the scientific milieu in which he worked and, on the other hand, to present a survey of his work not only in its historical context but especially in the frame of contemporary mathematics and physics. For one thing, this book contains expanded versions of the twelve invited lectures given at the International Christoffel Symposium, held on November 8 11, 1979 at Aachen and Monschau. For another, the scope of these papers has been broadened by soliciting some fourtyfive additional invited articles, concerned either with further aspects of the work of Christoffel or with specia lized topics in fields in which Christoffel had worked. This should give the reader a greater opportunity to appreciate the richness of Christoffel's contributions to the mathematical and physical sciences, and not only its immediate impact but also its subsequent infiuence. It can be discerned that Christoffel did basic work not only in differential geometry or, better still, in classical tensor analysis, thereby supplying the mathematical foundations of Einstein's theory of general relativity, but also in a variety of other areas of mathematics. The scope of Christoffel's work can be appreciated from the following synopsis of the thirteen chapters into which the festschrift is divided. Chap
Science in Western and Eastern civilization in Carolingian times(
Book
)
12 editions published in 1993 in 4 languages and held by 246 WorldCat member libraries worldwide
12 editions published in 1993 in 4 languages and held by 246 WorldCat member libraries worldwide
Linear spaces and approximation : proceedings of the conference held at the Oberwolfach Mathematical Research Institute, Black
Forest, August 2027, 1977 = Lineare Räume und Approximation : Abhandlungen zur Tagung im Mathematischen Forschungsinstitut
Oberwolfach, Schwarzwald, vom 20, bis 27. August 1977 by
Paul Leo Butzer(
Book
)
22 editions published in 1978 in 4 languages and held by 245 WorldCat member libraries worldwide
The publication of Oberwolfach conference books was initiated by Birkhauser Publishers in 1964 with the proceedings of the conference 'On Approximation Theory', conducted by P.L. Butzer (Aachen) and J. Korevaar (Amsterdam). Since that auspicious beginning, others of the Oberwolfach proceedings have appeared in Birkhauser's ISNM series. The present volume is the fifth * edited at Aachen in collaboration with an external institution. It once again ad dresses itself to the most recent results on approximation and operator theory, and includes 47 of the 48 lectures presented at Oberwolfach, as well as five articles subsequently submitted by V.A. Baskakov (Moscow), H. Esser (Aachen), G. Lumer (Mons), E.L. Stark (Aachen) and P.M. Tamrazov (Kiev). In addition, there is a section devoted to new and unsolved problems, based upon two special problem sessions augmented by later communications from the participants. Corresponding to the nature of the conference, the aim of the organizers was to solicit both specialized and survey papers, ranging in the broad area of classical and functional analysis, from approximation and interpolation theory to Fourier and harmonic analysis, and to the theory of function spaces and operators. The papers were supplemented by lectures on fields represented for the first time in our series of Oberwolfach Conferences, so for example, complex function theory or probability and sampling theory
22 editions published in 1978 in 4 languages and held by 245 WorldCat member libraries worldwide
The publication of Oberwolfach conference books was initiated by Birkhauser Publishers in 1964 with the proceedings of the conference 'On Approximation Theory', conducted by P.L. Butzer (Aachen) and J. Korevaar (Amsterdam). Since that auspicious beginning, others of the Oberwolfach proceedings have appeared in Birkhauser's ISNM series. The present volume is the fifth * edited at Aachen in collaboration with an external institution. It once again ad dresses itself to the most recent results on approximation and operator theory, and includes 47 of the 48 lectures presented at Oberwolfach, as well as five articles subsequently submitted by V.A. Baskakov (Moscow), H. Esser (Aachen), G. Lumer (Mons), E.L. Stark (Aachen) and P.M. Tamrazov (Kiev). In addition, there is a section devoted to new and unsolved problems, based upon two special problem sessions augmented by later communications from the participants. Corresponding to the nature of the conference, the aim of the organizers was to solicit both specialized and survey papers, ranging in the broad area of classical and functional analysis, from approximation and interpolation theory to Fourier and harmonic analysis, and to the theory of function spaces and operators. The papers were supplemented by lectures on fields represented for the first time in our series of Oberwolfach Conferences, so for example, complex function theory or probability and sampling theory
Functional analysis and approximation : proceedings of the conference held at the Mathematical Research Institute at Oberwolfach,
Black Forest, August 916, 1980 by
Paul Leo Butzer(
Book
)
21 editions published between 1981 and 2013 in English and held by 242 WorldCat member libraries worldwide
These Proceedings form a record of the lectures presented at the interna tional Conference on Functional Analysis and Approximation held at the Ober wolfach Mathematical Research Institute, August 916, 1980. They include 33 of the 38 invited conference papers, as well as three papers subsequently submitted in writing. Further, there is a report devoted to new and unsolved problems, based on two special sessions of the conference. The present volume is the sixth Oberwolfach Conference in Birkhauser's ISNM series to be edited at Aachen *. It is once again devoted to more significant results obtained in the wide areas of approximation theory, harmonic analysis, functional analysis, and operator theory during the past three years. Many of the papers solicited not only outline fundamental advances in their fields but also focus on interconnections between the various research areas. The papers in the present volume have been grouped into nine chapters. Chapter I, on operator theory, deals with maps on positive semidefinite opera tors, spectral bounds of semigroup operators, evolution equations of diffusion type, the spectral theory of propagators, and generalized inverses. Chapter II, on functional analysis, contains papers on modular approximation, interpolation spaces, and unconditional bases
21 editions published between 1981 and 2013 in English and held by 242 WorldCat member libraries worldwide
These Proceedings form a record of the lectures presented at the interna tional Conference on Functional Analysis and Approximation held at the Ober wolfach Mathematical Research Institute, August 916, 1980. They include 33 of the 38 invited conference papers, as well as three papers subsequently submitted in writing. Further, there is a report devoted to new and unsolved problems, based on two special sessions of the conference. The present volume is the sixth Oberwolfach Conference in Birkhauser's ISNM series to be edited at Aachen *. It is once again devoted to more significant results obtained in the wide areas of approximation theory, harmonic analysis, functional analysis, and operator theory during the past three years. Many of the papers solicited not only outline fundamental advances in their fields but also focus on interconnections between the various research areas. The papers in the present volume have been grouped into nine chapters. Chapter I, on operator theory, deals with maps on positive semidefinite opera tors, spectral bounds of semigroup operators, evolution equations of diffusion type, the spectral theory of propagators, and generalized inverses. Chapter II, on functional analysis, contains papers on modular approximation, interpolation spaces, and unconditional bases
Anniversary volume on approximation theory and functional analysis by
Paul Leo Butzer(
Book
)
23 editions published between 1984 and 2014 in English and German and held by 227 WorldCat member libraries worldwide
These Proceedings include 42 of the 49 invited conference papers, three papers sub mitted subsequently, and a report devoted to new and unsolved problems based on two special problem sessions and as augmented by later communications from the participants. In addition, there are four short accounts that emphasize the personality of the scholars to whom the proceedings are dedicated. Due to the large number of contributors, the length of the papers had to be restricted. This volume is again devoted to recent significant results obtained in approximation theory, harmonic analysis, functional analysis, and operator theory. The papers solicited include in addition survey articles that not only describe fundamental advances in their subfields, but many also emphasize basic interconnections between the various research areas. They tend to reflect the range of interests of the organizers and of their immediate colleagues and collaborators. The papers have been grouped according to subject matter into ten chapters. Chap ter I, on operator theory, is devoted to certain classes of operators such as contraction, hyponormal, and accretive operators, as well as to suboperators and semi groups of operators. Chapter II, on functional analysis, contains papers on function spaces, algebras, ideals, and generalized functions. Chapter III, on abstract approximation, is concerned with the comparison of approximation processes, the gliding hump method, certain inter polation spaces, and nwidths
23 editions published between 1984 and 2014 in English and German and held by 227 WorldCat member libraries worldwide
These Proceedings include 42 of the 49 invited conference papers, three papers sub mitted subsequently, and a report devoted to new and unsolved problems based on two special problem sessions and as augmented by later communications from the participants. In addition, there are four short accounts that emphasize the personality of the scholars to whom the proceedings are dedicated. Due to the large number of contributors, the length of the papers had to be restricted. This volume is again devoted to recent significant results obtained in approximation theory, harmonic analysis, functional analysis, and operator theory. The papers solicited include in addition survey articles that not only describe fundamental advances in their subfields, but many also emphasize basic interconnections between the various research areas. They tend to reflect the range of interests of the organizers and of their immediate colleagues and collaborators. The papers have been grouped according to subject matter into ten chapters. Chap ter I, on operator theory, is devoted to certain classes of operators such as contraction, hyponormal, and accretive operators, as well as to suboperators and semi groups of operators. Chapter II, on functional analysis, contains papers on function spaces, algebras, ideals, and generalized functions. Chapter III, on abstract approximation, is concerned with the comparison of approximation processes, the gliding hump method, certain inter polation spaces, and nwidths
Karl der Grosse und sein Nachwirken : 1200 Jahre Kultur und Wissenschaft in Europa by Colloquium Carolus Magnus(
Book
)
28 editions published between 1997 and 1998 in 4 languages and held by 169 WorldCat member libraries worldwide
28 editions published between 1997 and 1998 in 4 languages and held by 169 WorldCat member libraries worldwide
Approximationsprozesse und Interpolationsmethoden by
Paul Leo Butzer(
Book
)
16 editions published in 1968 in German and English and held by 112 WorldCat member libraries worldwide
16 editions published in 1968 in German and English and held by 112 WorldCat member libraries worldwide
Hilberttransformation, gebrochene Integration und Differentiation by
Paul Leo Butzer(
Book
)
11 editions published in 1968 in German and Undetermined and held by 98 WorldCat member libraries worldwide
Diese Monographie behandelt die eindimensionale Hilberttransformation und die ge brochene Integration auf der reellen Zahlengeraden. Da sich viele der Beweise auf die Fouriertransformation für LpFunktionen (1 ~ P ~ 2) stützen, haben wir in Kapitel 1 alles Nötige aus der Theorie der Fouriertransformation für Funktionen einer Veränder lichen systematisch zusammengestellt. Weiterhin haben wir uns erlaubt, die wohl bekannten Eigenschaften der Hilberttransformation ohne Beweis vorauszusetzen und weniger bekannte ausführlich zu beweisen. Der Schwerpunkt der Monographie liegt bei den Kapiteln 36, deren Ergebnisse zum großen Teil neu sind. Da in der Einleitung über die Problemstellung und über die Resultate näher berichtet wird, sei an dieser Stelle nur erwähnt, daß Ausgangspunkte unserer Überlegungen Arbeiten folgender Mathematiker sind: S. BOCHNER, J.L.B. COOPER, W. FELLER, G.H. HARDY, J.E. LITTLEWOOD, G.O. OKIKIOLU, M. RIESZ, E.C. TITCHMARSH und H. WEYL. Dadurch wird eine Einordnung unserer Ergebnisse gewährleistet. Unser besonderer Dank gilt Herrn Professor J.L.B. COOPER für viele fruchtbare Dis kussionen und wertvolle Ratschläge. Seine Vorträge im Aachener Kolloquium und seine Teilnahme an einer Tagung, die der erstgenannte Verfasser im MATHEMATISCHEN FORSCHUNGSINSTITUT OBERWOLFACH im August 1963 abgehalten hat, waren stets an regend. Die Verfasser danken den Herrn Dr. E. GÖRLICH und H. JOHNEN für manche kritischen Bemerkungen und für ihre Mithilfe bei der Durchsicht von Teilen des Manuskripts und der Korrekturen, ferner Frl. K. REIMERKELLNER, die das Manuskript mit großer Sorgfalt geschrieben hat, und dem Westdeutschen Verlag für sein Ent gegenkommen und die gute Ausstattung dieser Monographie
11 editions published in 1968 in German and Undetermined and held by 98 WorldCat member libraries worldwide
Diese Monographie behandelt die eindimensionale Hilberttransformation und die ge brochene Integration auf der reellen Zahlengeraden. Da sich viele der Beweise auf die Fouriertransformation für LpFunktionen (1 ~ P ~ 2) stützen, haben wir in Kapitel 1 alles Nötige aus der Theorie der Fouriertransformation für Funktionen einer Veränder lichen systematisch zusammengestellt. Weiterhin haben wir uns erlaubt, die wohl bekannten Eigenschaften der Hilberttransformation ohne Beweis vorauszusetzen und weniger bekannte ausführlich zu beweisen. Der Schwerpunkt der Monographie liegt bei den Kapiteln 36, deren Ergebnisse zum großen Teil neu sind. Da in der Einleitung über die Problemstellung und über die Resultate näher berichtet wird, sei an dieser Stelle nur erwähnt, daß Ausgangspunkte unserer Überlegungen Arbeiten folgender Mathematiker sind: S. BOCHNER, J.L.B. COOPER, W. FELLER, G.H. HARDY, J.E. LITTLEWOOD, G.O. OKIKIOLU, M. RIESZ, E.C. TITCHMARSH und H. WEYL. Dadurch wird eine Einordnung unserer Ergebnisse gewährleistet. Unser besonderer Dank gilt Herrn Professor J.L.B. COOPER für viele fruchtbare Dis kussionen und wertvolle Ratschläge. Seine Vorträge im Aachener Kolloquium und seine Teilnahme an einer Tagung, die der erstgenannte Verfasser im MATHEMATISCHEN FORSCHUNGSINSTITUT OBERWOLFACH im August 1963 abgehalten hat, waren stets an regend. Die Verfasser danken den Herrn Dr. E. GÖRLICH und H. JOHNEN für manche kritischen Bemerkungen und für ihre Mithilfe bei der Durchsicht von Teilen des Manuskripts und der Korrekturen, ferner Frl. K. REIMERKELLNER, die das Manuskript mit großer Sorgfalt geschrieben hat, und dem Westdeutschen Verlag für sein Ent gegenkommen und die gute Ausstattung dieser Monographie
Ein Operatorenkalkül zur Lösung gewöhnlicher und partieller Differenzengleichungssysteme von Funktionen diskreter Veränderlicher
und seine Anwendungen by
Paul Leo Butzer(
Book
)
6 editions published in 1965 in German and held by 60 WorldCat member libraries worldwide
6 editions published in 1965 in German and held by 60 WorldCat member libraries worldwide
Collected works = : Oeuvres scientifiques by
Charles Jean de La Vallée Poussin(
Book
)
25 editions published between 1952 and 2000 in 3 languages and held by 50 WorldCat member libraries worldwide
25 editions published between 1952 and 2000 in 3 languages and held by 50 WorldCat member libraries worldwide
Approximation und Interpolation durch verallgemeinerte Abtastsummen by
Paul Leo Butzer(
Book
)
6 editions published in 1977 in German and held by 46 WorldCat member libraries worldwide
6 editions published in 1977 in German and held by 46 WorldCat member libraries worldwide
Darstellungssätze für beschränkte lineare Funktionale im Zusammenhang mit Hausdorff, Stieltjes und HamburgerMomentenproblemen by
Paul Leo Butzer(
Book
)
8 editions published in 1975 in German and held by 33 WorldCat member libraries worldwide
In unserer Arbeit [7] werden beschrEinkte lineare Funktionale auf verschiedenen R~umen stetiger Funktionen untersucht und zwar die Gultig~eit von RieszDarstellungss~tzen. W~hrend wir uns dort auf stetige Funktionen beschr~nken, nehmen wir hier die R~ume Lebesgueintegrierbarer Funktionen hinzu. Ein Aspekt der obigen Arbeit ist der Zusammenhang zwischen dem BV[O, l]HausdorffMomentenproblem und dem C[O, l]RieszDar stellungssatz: einmal kann man den C[O, l]RieszSatz durch An wendung des BV[O, l]HausdorffMomentenproblems beweisen (vgl. [20], [39]), aber umgekehrt l~~t sich das HausdorffMomentenproblem Uber den RieszDarstellungssatz IBsen (vgl. [19], [25]). Es stellt sich daher die Frage, ob ein ~hnlicher . Zusammenhang nach gewiesen werden kann zwischen den RieszDarstellungss~tzen fUr verschiedene R~ume stetiger bzw. Lebesgueintegrierbarer Funk tionen und gewissen Momentenproblemen mit Belegungsfunktionen aus den dualen R~umen. Dazu wollen wir zun~chst einmal verschiedene Funktionenr~ume definieren. Fur reel Ie Zahlen a und b, a
8 editions published in 1975 in German and held by 33 WorldCat member libraries worldwide
In unserer Arbeit [7] werden beschrEinkte lineare Funktionale auf verschiedenen R~umen stetiger Funktionen untersucht und zwar die Gultig~eit von RieszDarstellungss~tzen. W~hrend wir uns dort auf stetige Funktionen beschr~nken, nehmen wir hier die R~ume Lebesgueintegrierbarer Funktionen hinzu. Ein Aspekt der obigen Arbeit ist der Zusammenhang zwischen dem BV[O, l]HausdorffMomentenproblem und dem C[O, l]RieszDar stellungssatz: einmal kann man den C[O, l]RieszSatz durch An wendung des BV[O, l]HausdorffMomentenproblems beweisen (vgl. [20], [39]), aber umgekehrt l~~t sich das HausdorffMomentenproblem Uber den RieszDarstellungssatz IBsen (vgl. [19], [25]). Es stellt sich daher die Frage, ob ein ~hnlicher . Zusammenhang nach gewiesen werden kann zwischen den RieszDarstellungss~tzen fUr verschiedene R~ume stetiger bzw. Lebesgueintegrierbarer Funk tionen und gewissen Momentenproblemen mit Belegungsfunktionen aus den dualen R~umen. Dazu wollen wir zun~chst einmal verschiedene Funktionenr~ume definieren. Fur reel Ie Zahlen a und b, a
New perspectives on approximation and sampling theory : festschrift in honor of Paul Butzer's 85th birthday by
Ahmed I Zayed(
Book
)
4 editions published in 2014 in English and held by 18 WorldCat member libraries worldwide
Paul Butzer, who is considered the academic father and grandfather of many prominent mathematicians, has established one of the best schools in approximation and sampling theory in the world. He is one of the leading figures in approximation, sampling theory, and harmonic analysis. Although on April 15, 2013, Paul Butzer turned 85 years old, remarkably, he is still an active research mathematician. In celebration of Paul Butzer?s 85th birthday, New Perspectives on Approximation and Sampling Theory is a collection of invited chapters on approximation, sampling, and harmonic analysis written by students, friends, colleagues, and prominent active mathematicians. Topics covered include approximation methods using wavelets, multiscale analysis, frames, and special functions. New Perspectives on Approximation and Sampling Theory requires basic knowledge of mathematical analysis, but efforts were made to keep the exposition clear and the chapters selfcontained. This volume will appeal to researchers and graduate students in mathematics, applied mathematics and engineering, in particular, engineers working in signal and image processing
4 editions published in 2014 in English and held by 18 WorldCat member libraries worldwide
Paul Butzer, who is considered the academic father and grandfather of many prominent mathematicians, has established one of the best schools in approximation and sampling theory in the world. He is one of the leading figures in approximation, sampling theory, and harmonic analysis. Although on April 15, 2013, Paul Butzer turned 85 years old, remarkably, he is still an active research mathematician. In celebration of Paul Butzer?s 85th birthday, New Perspectives on Approximation and Sampling Theory is a collection of invited chapters on approximation, sampling, and harmonic analysis written by students, friends, colleagues, and prominent active mathematicians. Topics covered include approximation methods using wavelets, multiscale analysis, frames, and special functions. New Perspectives on Approximation and Sampling Theory requires basic knowledge of mathematical analysis, but efforts were made to keep the exposition clear and the chapters selfcontained. This volume will appeal to researchers and graduate students in mathematics, applied mathematics and engineering, in particular, engineers working in signal and image processing
Dyadic Walsh analysis from 1924 onwards WalshGibbsButzer dyadic differentiation in science. a monograph based on articles
of the founding authors, reproduced in full by
Radomir S Stanković(
Book
)
5 editions published in 2015 in English and held by 4 WorldCat member libraries worldwide
The second volume of the two volumes book is dedicated to various extensions and generalizations of Dyadic (Walsh) analysis and related applications. Considered are dyadic derivatives on Vilenkin groups and various other Abelian and finite nonAbelian groups. Since some important results were developed in former Soviet Union and China, we provide overviews of former work in these countries. Further, we present translations of three papers that were initially published in Chinese. The presentation continues with chapters written by experts in the area presenting discussions of applications of these results in specific tasks in the area of signal processing and system theory. Efficient computing of related differential operators on contemporary hardware, including graphics processing units, is also considered, which makes the methods and techniques of dyadic analysis and generalizations computationally feasible. The volume 2 of the book ends with a chapter presenting open problems pointed out by several experts in the area
5 editions published in 2015 in English and held by 4 WorldCat member libraries worldwide
The second volume of the two volumes book is dedicated to various extensions and generalizations of Dyadic (Walsh) analysis and related applications. Considered are dyadic derivatives on Vilenkin groups and various other Abelian and finite nonAbelian groups. Since some important results were developed in former Soviet Union and China, we provide overviews of former work in these countries. Further, we present translations of three papers that were initially published in Chinese. The presentation continues with chapters written by experts in the area presenting discussions of applications of these results in specific tasks in the area of signal processing and system theory. Efficient computing of related differential operators on contemporary hardware, including graphics processing units, is also considered, which makes the methods and techniques of dyadic analysis and generalizations computationally feasible. The volume 2 of the book ends with a chapter presenting open problems pointed out by several experts in the area
Dyadic Walsh Analysis from 1924 Onwards WalshGibbsButzer Dyadic Differentiation in Science Volume 1 Foundations A Monograph
Based on Articles of the Founding Authors, Reproduced in Full by
Radomir S Stanković(
)
5 editions published in 2015 in English and held by 0 WorldCat member libraries worldwide
Dyadic (Walsh) analysis emerged as a new research area in applied mathematics and engineering in early seventies within attempts to provide answers to demands from practice related to application of spectral analysis of different classes of signals, including audio, video, sonar, and radar signals. In the meantime, it evolved in a mature mathematical discipline with fundamental results and important features providing basis for various applications. The book will provide fundamentals of the area through reprinting carefully selected earlier publications followed by overview of recent results concerning particular subjects in the area written by experts, most of them being founders of the field, and some of their followers. In this way, this first volume of the two volume book offers a rather complete coverage of the development of dyadic Walsh analysis, and provides a deep insight into its mathematical foundations necessary for consideration of generalizations and applications that are the subject of the second volume. The presented theory is quite sufficient to be a basis for further research in the subject area as well as to be applied in solving certain new problems or improving existing solutions for tasks in the areas which motivated development of the dyadic analysis
5 editions published in 2015 in English and held by 0 WorldCat member libraries worldwide
Dyadic (Walsh) analysis emerged as a new research area in applied mathematics and engineering in early seventies within attempts to provide answers to demands from practice related to application of spectral analysis of different classes of signals, including audio, video, sonar, and radar signals. In the meantime, it evolved in a mature mathematical discipline with fundamental results and important features providing basis for various applications. The book will provide fundamentals of the area through reprinting carefully selected earlier publications followed by overview of recent results concerning particular subjects in the area written by experts, most of them being founders of the field, and some of their followers. In this way, this first volume of the two volume book offers a rather complete coverage of the development of dyadic Walsh analysis, and provides a deep insight into its mathematical foundations necessary for consideration of generalizations and applications that are the subject of the second volume. The presented theory is quite sufficient to be a basis for further research in the subject area as well as to be applied in solving certain new problems or improving existing solutions for tasks in the areas which motivated development of the dyadic analysis
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Related Identities
 SzőkefalviNagy, Béla 19131998 Editor Creator
 Mathematisches Forschungsinstitut Oberwolfach Editor
 Nessel, Rolf J. 1936 Editor
 Berens, Hubert
 Stanković, Radomir S. Author Editor
 Schipp, F. (Ferenc) 1939
 Wade, W. R.
 Kahane, Jean Pierre Editor
 Korevaar, Jacob 1923 Author Editor Creator
 Zayed, Ahmed I. Author Editor
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Associated Subjects
Algebraic spaces Algebras, Linear Approximation theory Banach spaces Calculus, Operational Charlemagne,Emperor, Christoffel, Elwin Bruno, Civilization Computer scienceMathematics Difference equations Europe Fourier analysis Fourier series Fourier transformations Functional analysis Functions Functions, Special Functions of real variables Gibbs' equation Global analysis (Mathematics) Group theory Harmonic analysis Influence (Literary, artistic, etc.) Integrals Interpolation La Vallée Poussin, Charles Jean de, Linear operators Mathematical analysis Mathematics Moment spaces Number theory Numerical analysis Operator theory Physical sciences Sampling (Statistics) Science Science, Medieval Semigroups Vector spaces Walsh functions
Alternative Names
Butzer, P.
Butzer, P. 1928
Butzer, P. L.
Butzer, P.L. 1928
Butzer, P. L. (Paul Leo), 1928
Butzer , Paul
Butzer, Paul 1928
Butzer, Paul L.
Butzer, Paul L. 1928
Butzer, Paul L. (Paul Leo), 1928
Butzer, Paul Leo 1928
Paul Butzer deutscher Mathematiker
Paul Butzer Duits wiskundige
Paul Butzer German mathematician and historian of mathematics
Paul Butzer matematico tedesco
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German (103)
Multiple languages (13)
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