Berg, Christian 1944
Overview
Works:  21 works in 108 publications in 6 languages and 1,801 library holdings 

Genres:  Conference papers and proceedings 
Roles:  Author, Editor, Composer 
Publication Timeline
.
Most widely held works by
Christian Berg
Potential theory, Copenhagen 1979 : proceedings of a colloquium held in Copenhagen, May 1418, 1979 by
Christian Berg(
Book
)
24 editions published in 1980 in 3 languages and held by 542 WorldCat member libraries worldwide
24 editions published in 1980 in 3 languages and held by 542 WorldCat member libraries worldwide
Harmonic analysis on semigroups : theory of positive definite and related functions by
Christian Berg(
Book
)
18 editions published between 1984 and 2012 in English and held by 531 WorldCat member libraries worldwide
The Fourier transform and the Laplace transform of a positive measure share, together with its moment sequence, a positive definiteness property which under certain regularity assumptions is characteristic for such expressions. This is formulated in exact terms in the famous theorems of Bochner, BernsteinWidder and Hamburger. All three theorems can be viewed as special cases of a general theorem about functions qJ on abelian semigroups with involution (S, +, *) which are positive definite in the sense that the matrix (qJ(sJ + Sk{raquo} is positive definite for all finite choices of elements St ..., Sn from S. The three basic results mentioned above correspond to (~, +, x* = x), ([0, 00[, +, x* = x) and (No, +, n* = n). The purpose of this book is to provide a treatment of these positive definite functions on abelian semigroups with involution. In doing so we also discuss related topics such as negative definite functions, completely mono tone functions and Hoeffdingtype inequalities. We view these subjects as important ingredients of harmonic analysis on semigroups. It has been our aim, simultaneously, to write a book which can serve as a textbook for an advanced graduate course, because we feel that the notion of positive definiteness is an important and basic notion which occurs in mathematics as often as the notion of a Hilbert space
18 editions published between 1984 and 2012 in English and held by 531 WorldCat member libraries worldwide
The Fourier transform and the Laplace transform of a positive measure share, together with its moment sequence, a positive definiteness property which under certain regularity assumptions is characteristic for such expressions. This is formulated in exact terms in the famous theorems of Bochner, BernsteinWidder and Hamburger. All three theorems can be viewed as special cases of a general theorem about functions qJ on abelian semigroups with involution (S, +, *) which are positive definite in the sense that the matrix (qJ(sJ + Sk{raquo} is positive definite for all finite choices of elements St ..., Sn from S. The three basic results mentioned above correspond to (~, +, x* = x), ([0, 00[, +, x* = x) and (No, +, n* = n). The purpose of this book is to provide a treatment of these positive definite functions on abelian semigroups with involution. In doing so we also discuss related topics such as negative definite functions, completely mono tone functions and Hoeffdingtype inequalities. We view these subjects as important ingredients of harmonic analysis on semigroups. It has been our aim, simultaneously, to write a book which can serve as a textbook for an advanced graduate course, because we feel that the notion of positive definiteness is an important and basic notion which occurs in mathematics as often as the notion of a Hilbert space
Potential theory on locally compact Abelian groups by
Christian Berg(
Book
)
17 editions published between 1975 and 1976 in English and held by 444 WorldCat member libraries worldwide
Classical potential theory can be roughly characterized as the study of Newtonian potentials and the Laplace operator on the Euclidean space JR3. It was discovered around 1930 that there is a profound connection between classical potential 3 theory and the theory of Brownian motion in JR . The Brownian motion is determined by its semigroup of transition probabilities, the Brownian semigroup, and the connection between classical potential theory and the theory of Brownian motion can be described analytically in the following way: The Laplace operator is the infinitesimal generator for the Brownian semigroup and the Newtonian potential kernel is the" integral" of the Brownian semigroup with respect to time. This connection between classical potential theory and the theory of Brownian motion led Hunt (cf. Hunt [2]) to consider general "potential theories" defined in terms of certain stochastic processes or equivalently in terms of certain semi groups of operators on spaces of functions. The purpose of the present exposition is to study such general potential theories where the following aspects of classical potential theory are preserved: (i) The theory is defined on a locally compact abelian group. (ii) The theory is translation invariant in the sense that any translate of a potential or a harmonic function is again a potential, respectively a harmonic function; this property of classical potential theory can also be expressed by saying that the Laplace operator is a differential operator with constant co efficients
17 editions published between 1975 and 1976 in English and held by 444 WorldCat member libraries worldwide
Classical potential theory can be roughly characterized as the study of Newtonian potentials and the Laplace operator on the Euclidean space JR3. It was discovered around 1930 that there is a profound connection between classical potential 3 theory and the theory of Brownian motion in JR . The Brownian motion is determined by its semigroup of transition probabilities, the Brownian semigroup, and the connection between classical potential theory and the theory of Brownian motion can be described analytically in the following way: The Laplace operator is the infinitesimal generator for the Brownian semigroup and the Newtonian potential kernel is the" integral" of the Brownian semigroup with respect to time. This connection between classical potential theory and the theory of Brownian motion led Hunt (cf. Hunt [2]) to consider general "potential theories" defined in terms of certain stochastic processes or equivalently in terms of certain semi groups of operators on spaces of functions. The purpose of the present exposition is to study such general potential theories where the following aspects of classical potential theory are preserved: (i) The theory is defined on a locally compact abelian group. (ii) The theory is translation invariant in the sense that any translate of a potential or a harmonic function is again a potential, respectively a harmonic function; this property of classical potential theory can also be expressed by saying that the Laplace operator is a differential operator with constant co efficients
The Harald Bohr centenary : proceedings of a symposium held in Copenhagen, April 2425, 1987 by Bohr Harald Centenary(
Book
)
9 editions published between 1989 and 1990 in English and held by 77 WorldCat member libraries worldwide
9 editions published between 1989 and 1990 in English and held by 77 WorldCat member libraries worldwide
Potential Theory Copenhagen 1979 : Proceedings of a Colloquium Held in Copenhagen, May 1418, 1979(
)
1 edition published in 1980 in English and held by 41 WorldCat member libraries worldwide
1 edition published in 1980 in English and held by 41 WorldCat member libraries worldwide
Potential theory on locally compact Abelian groups by
Christian Berg(
Book
)
2 editions published in 1975 in Undetermined and English and held by 36 WorldCat member libraries worldwide
2 editions published in 1975 in Undetermined and English and held by 36 WorldCat member libraries worldwide
Potential theory Copenhagen 1979 : proceedings of a colloquium ; Copenhagen, May 1418, 1979 by
Christian Berg(
Book
)
12 editions published between 1979 and 2008 in 3 languages and held by 27 WorldCat member libraries worldwide
12 editions published between 1979 and 2008 in 3 languages and held by 27 WorldCat member libraries worldwide
Schlupps der Handwerksbursch : Mären und Schnuren by
Christian Berg(
)
7 editions published between 1920 and 1947 in German and held by 25 WorldCat member libraries worldwide
7 editions published between 1920 and 1947 in German and held by 25 WorldCat member libraries worldwide
Potential theory : Copenhagen 1979 ; proceedings of a colloquium, held in Copenhagen, May 1418, 1979(
Book
)
1 edition published in 1980 in English and held by 24 WorldCat member libraries worldwide
1 edition published in 1980 in English and held by 24 WorldCat member libraries worldwide
Addenda et emendanda ad Hemiptera Argentina by
Christian Berg(
)
3 editions published in 1914 in Latin and held by 18 WorldCat member libraries worldwide
3 editions published in 1914 in Latin and held by 18 WorldCat member libraries worldwide
Ein Netzwerk für botanischen Naturschutz : neue Herausforderungen für die Botanikerinnen und Botaniker Deutschlands(
Book
)
2 editions published in 2006 in German and held by 17 WorldCat member libraries worldwide
2 editions published in 2006 in German and held by 17 WorldCat member libraries worldwide
Corps convexes et potentiels sphériques by
Christian Berg(
Book
)
1 edition published in 1969 in Undetermined and held by 7 WorldCat member libraries worldwide
1 edition published in 1969 in Undetermined and held by 7 WorldCat member libraries worldwide
Nogle Sprogbemaerkninger knyttede tel en Kommentar til Xenophons Hieron by
Christian Berg(
Book
)
1 edition published in 1852 in Danish and held by 2 WorldCat member libraries worldwide
1 edition published in 1852 in Danish and held by 2 WorldCat member libraries worldwide
SHRIMP constraints on sediment provenance and transport history on the Mesozoic Statfjord Formation, North Sea by A. C Morton(
)
in English and held by 2 WorldCat member libraries worldwide
in English and held by 2 WorldCat member libraries worldwide
Blood parameters of goats, Artesia Village, Kagatleng Agricultural District, Botswana by R Gray(
Book
)
1 edition published in 1988 in English and held by 2 WorldCat member libraries worldwide
1 edition published in 1988 in English and held by 2 WorldCat member libraries worldwide
Proceedings of the Seventh International Symposium on Orthogonal Polynomials, Special Functions and Applications : Copenhagen,
Denmark, 1822 August 2003 by Special Functions and Their Applications. <7, 2003, København> International Symposium on Orthogonal Polynomials(
Book
)
3 editions published in 2005 in English and held by 2 WorldCat member libraries worldwide
3 editions published in 2005 in English and held by 2 WorldCat member libraries worldwide
Corps convexes et potentiels sphériques by
Christian Berg(
Book
)
1 edition published in 1969 in Danish and held by 1 WorldCat member library worldwide
1 edition published in 1969 in Danish and held by 1 WorldCat member library worldwide
Keep you kimi by
Nilokheri Haryana Institute of Rural Development(
Recording
)
in Undetermined and held by 1 WorldCat member library worldwide
in Undetermined and held by 1 WorldCat member library worldwide
Potential theory on locally compact abelian groups by
Christian Berg(
)
1 edition published in 1975 in English and held by 1 WorldCat member library worldwide
1 edition published in 1975 in English and held by 1 WorldCat member library worldwide
Notas Sinonimicas acerca de algunos Coleópteros y Lepidópteros by
Christian Berg(
Book
)
1 edition published in 1883 in Spanish and held by 1 WorldCat member library worldwide
1 edition published in 1883 in Spanish and held by 1 WorldCat member library worldwide
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Audience Level
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Related Identities
 Forst, Gunnar 1946 Editor
 Fuglede, Bent Author Editor
 Ressel, Paul
 Christensen, Jens Peter Reus
 DanishFrench Society for Scientific Research and Exchange
 Bohr, Harald August 18871951 Honoree
 Kongelige Danske videnskabernes selskab
 Hövelmann, Thomas Redactor
 Fuglede, G.
 Colloquium on potential theory, Copenhagen, 1979
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Associated Subjects
Almost periodic functions Argentina BloodAnalysis Bohr, Harald August, Fools and jesters Functions, Special Germany GoatsFeeding and feeds Harmonic analysis Locally compact Abelian groups Mathematics Membracidae Orthogonal polynomials Periodic functions Positivedefinite functions Potential theory (Mathematics) Semigroups Tales Topological groups Xenophon