Pinkus, Allan 1946
Overview
Works:  56 works in 208 publications in 3 languages and 2,663 library holdings 

Genres:  Conference papers and proceedings 
Roles:  Author, Editor 
Classifications:  QA221, 511.4 
Publication Timeline
.
Most widely held works by
Allan Pinkus
Fourier series and integral transforms by
Allan Pinkus(
Book
)
17 editions published between 1997 and 1999 in English and held by 449 WorldCat member libraries worldwide
The aim of this book is to provide the reader with a basic understanding of Fourier series, Fourier transforms and Laplace transforms. The book is an expanded and polished version of the authors' notes for a one semester course, for students of mathematics, electrical engineering, physics and computer science. Prerequisites for readers of this book are a basic course in both calculus and linear algebra. Otherwise the material is selfcontained with numerous exercises and various examples of applications
17 editions published between 1997 and 1999 in English and held by 449 WorldCat member libraries worldwide
The aim of this book is to provide the reader with a basic understanding of Fourier series, Fourier transforms and Laplace transforms. The book is an expanded and polished version of the authors' notes for a one semester course, for students of mathematics, electrical engineering, physics and computer science. Prerequisites for readers of this book are a basic course in both calculus and linear algebra. Otherwise the material is selfcontained with numerous exercises and various examples of applications
Nwidths in approximation theory by
Allan Pinkus(
Book
)
18 editions published between 1984 and 1985 in 4 languages and held by 402 WorldCat member libraries worldwide
My original introduction to this subject was through conservations, and ultimate ly joint work with C.A. Micchelli. I am grateful to him and to Profs. C. de Boor, E.W. Cheney, S.D. Fisher and A.A. Melkman who read various portions of the manuscript and whose suggestions were most helpful. Errors in accuracy and omissions are totally my responsibility. I would like to express my appreciation to the SERC of Great Britain and to the Department of Mathematics of the University of Lancaster for the year spent there during which large portions of the manuscript were written, and also to the European Research Office of the U.S. Army for its financial support of my research endeavors. Thanks are also due to Marion Marks who typed portions of the manuscript. Haifa, 1984 Allan Pinkus Table of Contents 1 Chapter I. Introduction ... Chapter II. Basic Properties of nWidths . 9 1. Properties of d           9 n 15 2. Existence of Optimal Subspaces for d  n n 17 3. Properties of d       20 4. Properties of b       n 5. Inequalities Between nWidths 22 n 6. Duality Between d and d   27 n 7. nWidths of Mappings of the Unit Ball 29 8. Some Relationships Between dn(T), dn(T) and bn(T) . 32 37 Notes and References
18 editions published between 1984 and 1985 in 4 languages and held by 402 WorldCat member libraries worldwide
My original introduction to this subject was through conservations, and ultimate ly joint work with C.A. Micchelli. I am grateful to him and to Profs. C. de Boor, E.W. Cheney, S.D. Fisher and A.A. Melkman who read various portions of the manuscript and whose suggestions were most helpful. Errors in accuracy and omissions are totally my responsibility. I would like to express my appreciation to the SERC of Great Britain and to the Department of Mathematics of the University of Lancaster for the year spent there during which large portions of the manuscript were written, and also to the European Research Office of the U.S. Army for its financial support of my research endeavors. Thanks are also due to Marion Marks who typed portions of the manuscript. Haifa, 1984 Allan Pinkus Table of Contents 1 Chapter I. Introduction ... Chapter II. Basic Properties of nWidths . 9 1. Properties of d           9 n 15 2. Existence of Optimal Subspaces for d  n n 17 3. Properties of d       20 4. Properties of b       n 5. Inequalities Between nWidths 22 n 6. Duality Between d and d   27 n 7. nWidths of Mappings of the Unit Ball 29 8. Some Relationships Between dn(T), dn(T) and bn(T) . 32 37 Notes and References
On L1approximation by
Allan Pinkus(
Book
)
24 editions published between 1985 and 2008 in 3 languages and held by 352 WorldCat member libraries worldwide
24 editions published between 1985 and 2008 in 3 languages and held by 352 WorldCat member libraries worldwide
Totally positive matrices by
Allan Pinkus(
Book
)
17 editions published between 2009 and 2010 in English and held by 308 WorldCat member libraries worldwide
"Totally positive matrices constitute a particular class of matrices, the study of which was initiated by analysts because of its many applications in diverse areas. This modern account of the subject is comprehensive and thorough, with careful treatment of the central properties of totally positive matrices, full proofs and a complete bibliography. The history of the subject is also described: in particular, the book ends with a tribute to the four people who have made the most notable contributions to the history of total positivity: I.J. Schoenberg, M.G. Krein, F.R. Gantmacher and S. Karlin. This monograph will appeal to those with an interest in matrix theory, to those who use or have used total positivity, and to anyone who wishes to learn about this rich and interesting subject"Provided by publisher
17 editions published between 2009 and 2010 in English and held by 308 WorldCat member libraries worldwide
"Totally positive matrices constitute a particular class of matrices, the study of which was initiated by analysts because of its many applications in diverse areas. This modern account of the subject is comprehensive and thorough, with careful treatment of the central properties of totally positive matrices, full proofs and a complete bibliography. The history of the subject is also described: in particular, the book ends with a tribute to the four people who have made the most notable contributions to the history of total positivity: I.J. Schoenberg, M.G. Krein, F.R. Gantmacher and S. Karlin. This monograph will appeal to those with an interest in matrix theory, to those who use or have used total positivity, and to anyone who wishes to learn about this rich and interesting subject"Provided by publisher
Foundations of computational mathematics, Hong Kong 2008 by
Felipe Cucker(
Book
)
11 editions published in 2009 in English and held by 188 WorldCat member libraries worldwide
This volume is a collection of articles based on the plenary talks presented at the 2008 Society for the Foundations of Computational Mathematics meeting in Hong Kong. The talks were given by some of the foremost world authorities in computational mathematics. The topics covered reflect the breadth of research within the area as well as the richness and fertility of interactions between seemingly unrelated branches of pure and applied mathematics. As a result, this volume will be of interest to researchers in the field of computational mathematics and also to nonexperts who wish to gain some insight into the state of the art in this active and significant field
11 editions published in 2009 in English and held by 188 WorldCat member libraries worldwide
This volume is a collection of articles based on the plenary talks presented at the 2008 Society for the Foundations of Computational Mathematics meeting in Hong Kong. The talks were given by some of the foremost world authorities in computational mathematics. The topics covered reflect the breadth of research within the area as well as the richness and fertility of interactions between seemingly unrelated branches of pure and applied mathematics. As a result, this volume will be of interest to researchers in the field of computational mathematics and also to nonexperts who wish to gain some insight into the state of the art in this active and significant field
Ridge functions by
Allan Pinkus(
Book
)
13 editions published between 2015 and 2016 in English and held by 157 WorldCat member libraries worldwide
Ridge functions are a rich class of simple multivariate functions which have found applications in a variety of areas. These include partial differential equations (where they are sometimes termed 'plane waves'), computerised tomography, projection pursuit in the analysis of large multivariate data sets, the MLP model in neural networks, Waring's problem over linear forms, and approximation theory. Ridge Functions is the first book devoted to studying them as entities in and of themselves. The author describes their central properties and provides a solid theoretical foundation for researchers working in areas such as approximation or data science. He also includes an extensive bibliography and discusses some of the unresolved questions that may set the course for future research in the field
13 editions published between 2015 and 2016 in English and held by 157 WorldCat member libraries worldwide
Ridge functions are a rich class of simple multivariate functions which have found applications in a variety of areas. These include partial differential equations (where they are sometimes termed 'plane waves'), computerised tomography, projection pursuit in the analysis of large multivariate data sets, the MLP model in neural networks, Waring's problem over linear forms, and approximation theory. Ridge Functions is the first book devoted to studying them as entities in and of themselves. The author describes their central properties and provides a solid theoretical foundation for researchers working in areas such as approximation or data science. He also includes an extensive bibliography and discusses some of the unresolved questions that may set the course for future research in the field
Progress in approximation theory(
Book
)
9 editions published in 1991 in English and held by 155 WorldCat member libraries worldwide
9 editions published in 1991 in English and held by 155 WorldCat member libraries worldwide
Foundations of computational mathematics, Budapest 2011 by
Foundations of Computational Mathematics (Conference)(
Book
)
5 editions published between 2012 and 2013 in English and held by 11 WorldCat member libraries worldwide
The Foundations of Computational Mathematics meetings are a platform for crossfertilisation between numerical analysis, mathematics and computer science. This volume is a collection of articles based on plenary presentations, given at the 2011 meeting, by some of the world's foremost authorities in computational mathematics. The topics covered reflect the breadth of research within the area as well as the richness of interactions between seemingly unrelated branches of pure and applied mathematics. As a result this volume will be of interest to researchers in the field of computational mathematics and also to nonexperts who wish to gain some insight into the state of the art in this active and significant field
5 editions published between 2012 and 2013 in English and held by 11 WorldCat member libraries worldwide
The Foundations of Computational Mathematics meetings are a platform for crossfertilisation between numerical analysis, mathematics and computer science. This volume is a collection of articles based on plenary presentations, given at the 2011 meeting, by some of the world's foremost authorities in computational mathematics. The topics covered reflect the breadth of research within the area as well as the richness of interactions between seemingly unrelated branches of pure and applied mathematics. As a result this volume will be of interest to researchers in the field of computational mathematics and also to nonexperts who wish to gain some insight into the state of the art in this active and significant field
On Lapproximation by
Allan Pinkus(
Book
)
2 editions published in 1989 in English and held by 10 WorldCat member libraries worldwide
2 editions published in 1989 in English and held by 10 WorldCat member libraries worldwide
Inverses of infinite sign regular matrices by
Carl De Boor(
Book
)
5 editions published in 1980 in English and held by 7 WorldCat member libraries worldwide
Let A be an infinite sign regular (SR) matrix which can be viewed as a bounded linear operator from L sub infinity to itself. It is proved here that if the range of A contains the sequence (...,1,1,1,1 ...), then A is onto. If (inverse of A) exists then D (inverse of A) D is also SR, where D is the diagonal matrix with diagonal entries alternately 1 and 1. In case A is totally positive (TP), then D (inverse of A) D is also TP under additional assumptions on A. (Author)
5 editions published in 1980 in English and held by 7 WorldCat member libraries worldwide
Let A be an infinite sign regular (SR) matrix which can be viewed as a bounded linear operator from L sub infinity to itself. It is proved here that if the range of A contains the sequence (...,1,1,1,1 ...), then A is onto. If (inverse of A) exists then D (inverse of A) D is also SR, where D is the diagonal matrix with diagonal entries alternately 1 and 1. In case A is totally positive (TP), then D (inverse of A) D is also TP under additional assumptions on A. (Author)
A factorization of totally positive band matrices by
Carl De Boor(
Book
)
4 editions published in 1980 in English and held by 6 WorldCat member libraries worldwide
Every nonsingular totally positive mbanded matrix is shown to be the product of m totally positive onebanded matrices and, therefore, the limit of strictly mbanded matrices. This result is then extended to (bi) infinite 'nonsingular', totally positive matrices. In the process, such matrices are shown to possess at least one diagonal whose principal sections are all nonzero.(Author)
4 editions published in 1980 in English and held by 6 WorldCat member libraries worldwide
Every nonsingular totally positive mbanded matrix is shown to be the product of m totally positive onebanded matrices and, therefore, the limit of strictly mbanded matrices. This result is then extended to (bi) infinite 'nonsingular', totally positive matrices. In the process, such matrices are shown to possess at least one diagonal whose principal sections are all nonzero.(Author)
A simple proof of the HobbyRice theorem by
Allan Pinkus(
Book
)
6 editions published in 1976 in English and held by 5 WorldCat member libraries worldwide
This paper presents a simple proof of the HobbyRice theorem, and a matrix version of the above theorem
6 editions published in 1976 in English and held by 5 WorldCat member libraries worldwide
This paper presents a simple proof of the HobbyRice theorem, and a matrix version of the above theorem
Structure of Invertible (Bi)infinite Totally Positive Matrices by
Carl De Boor(
Book
)
3 editions published in 1981 in English and held by 4 WorldCat member libraries worldwide
An l subinfinityinvertible nonfinite totally positive matrix A is shown to have one and only one main diagonal. This means that exactly one diagonal of A has the property that all finite sections of A principal with respect to this diagonal are invertible and their inverses converge boundedly and entrywise to A to the 1 power. This is shown to imply restrictions on the possible shapes of such a matrix. In the proof, such a matrix is also shown to have a l subinfinity invertible LDU factorization. In addition, decay of the entries of such a matrix away from the main diagonal is demonstrated. It is also shown that a bounded signregular matrix carrying some bounded sequence to a uniformly alternating sequence must have all its columns in c sub o. (Author)
3 editions published in 1981 in English and held by 4 WorldCat member libraries worldwide
An l subinfinityinvertible nonfinite totally positive matrix A is shown to have one and only one main diagonal. This means that exactly one diagonal of A has the property that all finite sections of A principal with respect to this diagonal are invertible and their inverses converge boundedly and entrywise to A to the 1 power. This is shown to imply restrictions on the possible shapes of such a matrix. In the proof, such a matrix is also shown to have a l subinfinity invertible LDU factorization. In addition, decay of the entries of such a matrix away from the main diagonal is demonstrated. It is also shown that a bounded signregular matrix carrying some bounded sequence to a uniformly alternating sequence must have all its columns in c sub o. (Author)
Descartes systems from corner cutting by
Charles A Micchelli(
Book
)
2 editions published in 1989 in English and held by 3 WorldCat member libraries worldwide
Abstract: "This paper demonstrates that Descartes Systems can be conveniently generated from matrix subdivision algorithms determined by totally positive matrices."
2 editions published in 1989 in English and held by 3 WorldCat member libraries worldwide
Abstract: "This paper demonstrates that Descartes Systems can be conveniently generated from matrix subdivision algorithms determined by totally positive matrices."
Backward Error Analysis for Totally Positive Linear Systems by
Carl De Boor(
Book
)
4 editions published in 1976 in English and held by 3 WorldCat member libraries worldwide
A novel formulation of the results of Wilkinson's backward error analysis allows the conclusion that partial pivoting is not necessary when solving totally positive linear systems. This saves storage and time when computing spline interpolants
4 editions published in 1976 in English and held by 3 WorldCat member libraries worldwide
A novel formulation of the results of Wilkinson's backward error analysis allows the conclusion that partial pivoting is not necessary when solving totally positive linear systems. This saves storage and time when computing spline interpolants
Spectral Properties and Oscillation Theorems for Mixed BoundaryValue Problems of SturmLiouville Type by
Joe Won Lee(
Book
)
3 editions published in 1976 in English and held by 3 WorldCat member libraries worldwide
This paper presents analogues of the spectral and oscillatory properties exhibited by classical SturmLiouville systems for certain mixed boundary value problems that include periodic boundary conditions as a special case. These mixed boundaryvalue problems have Green's functions which are sign consistent for all even and/or odd orders. (Author)
3 editions published in 1976 in English and held by 3 WorldCat member libraries worldwide
This paper presents analogues of the spectral and oscillatory properties exhibited by classical SturmLiouville systems for certain mixed boundary value problems that include periodic boundary conditions as a special case. These mixed boundaryvalue problems have Green's functions which are sign consistent for all even and/or odd orders. (Author)
Foundations of computational mathematics, Santander 2005 by
L. M Pardo(
Book
)
4 editions published in 2006 in English and held by 2 WorldCat member libraries worldwide
This volume is a collection of articles based on the plenary talks presented at the 2005 meeting in Santander of the Society for the Foundations of Computational Mathematics. The talks were given by some of the foremost world authorities in computational mathematics. The topics covered reflect the breadth of research within the area as well as the richness and fertility of interactions between seemingly unrelated branches of pure and applied mathematics. As a result this volume will be of interest to researchers in the field of computational mathematics and also to nonexperts who wish to gain some insight into the state of the art in this active and significant field
4 editions published in 2006 in English and held by 2 WorldCat member libraries worldwide
This volume is a collection of articles based on the plenary talks presented at the 2005 meeting in Santander of the Society for the Foundations of Computational Mathematics. The talks were given by some of the foremost world authorities in computational mathematics. The topics covered reflect the breadth of research within the area as well as the richness and fertility of interactions between seemingly unrelated branches of pure and applied mathematics. As a result this volume will be of interest to researchers in the field of computational mathematics and also to nonexperts who wish to gain some insight into the state of the art in this active and significant field
Multivariate approximation and applications by
N Dyn(
Book
)
3 editions published between 2001 and 2010 in English and held by 1 WorldCat member library worldwide
Approximation theory in the multivariate setting has many applications including numerical analysis, wavelet analysis, signal processing, geographic information systems, computer aided geometric design and computer graphics. This advanced introduction to multivariate approximation and related topics consists of nine articles written by leading experts surveying many of the new ideas and their applications. Each article takes the reader to the forefront of research and ends with a comprehensive bibliography
3 editions published between 2001 and 2010 in English and held by 1 WorldCat member library worldwide
Approximation theory in the multivariate setting has many applications including numerical analysis, wavelet analysis, signal processing, geographic information systems, computer aided geometric design and computer graphics. This advanced introduction to multivariate approximation and related topics consists of nine articles written by leading experts surveying many of the new ideas and their applications. Each article takes the reader to the forefront of research and ends with a comprehensive bibliography
Cambridge Tracts in Mathematics, Volume 92 by
Allan Pinkus(
)
1 edition published in 2011 in English and held by 0 WorldCat member libraries worldwide
1 edition published in 2011 in English and held by 0 WorldCat member libraries worldwide
Encyclopaedia of mathematics. Supplement III by
Shreeram Shankar Abhyankar(
)
1 edition published in 2002 in English and held by 0 WorldCat member libraries worldwide
This is the third supplementary volume to Kluwer's highly acclaimed twelvevolume Encyclopaedia of Mathematics. This additional volume contains nearly 500 new entries written by experts and covers developments and topics not included in the previous volumes. These entries are arranged alphabetically throughout and a detailed index is included. This supplementary volume enhances the existing twelve volumes, and together, these thirteen volumes represent the most authoritative, comprehensive and uptodate Encyclopaedia of Mathematics available
1 edition published in 2002 in English and held by 0 WorldCat member libraries worldwide
This is the third supplementary volume to Kluwer's highly acclaimed twelvevolume Encyclopaedia of Mathematics. This additional volume contains nearly 500 new entries written by experts and covers developments and topics not included in the previous volumes. These entries are arranged alphabetically throughout and a detailed index is included. This supplementary volume enhances the existing twelve volumes, and together, these thirteen volumes represent the most authoritative, comprehensive and uptodate Encyclopaedia of Mathematics available
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Related Identities
 Zafrany, Samy 1959
 Todd, Michael J. 1947 Editor
 Cucker, Felipe 1958 Author Editor
 Nevai, Paul G. 1948 Editor
 Boley, D. L.
 Huang, Y.Z
 Abhyankar, S. S. Author
 Silbermann, B.
 Ramm, A. G.
 Piotrowski, Z.
Associated Subjects
Approximation theory Computer graphics Fourier series Functional analysis Function spaces Global analysis (Mathematics) Infinite matrices Integral transforms Least absolute deviations (Statistics) Linear operators Mathematical optimization Mathematics MathematicsData processing Matrices Matrix inversion Multivariate analysis Numbers, Real Numerical analysis