Harmonic Analysis on Semigroups: Theory of Positive Definite and Related Functions
Saved in:
| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
New York, NY
Springer New York
1984
|
| Series: | Graduate Texts in Mathematics
100 |
| Subjects: | |
| Links: | https://doi.org/10.1007/978-1-4612-1128-0 |
| Item Description: | 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, Bernstein-Widder 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» 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 Hoeffding-type 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 |
| Physical Description: | 1 Online-Ressource (X, 292 p) |
| ISBN: | 9781461211280 9781461270171 |
| ISSN: | 0072-5285 |
| DOI: | 10.1007/978-1-4612-1128-0 |
Staff View
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| 245 | 1 | 0 | |a Harmonic Analysis on Semigroups |b Theory of Positive Definite and Related Functions |c by Christian Berg, Jens Peter Reus Christensen, Paul Ressel |
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| 500 | |a 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, Bernstein-Widder 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» 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 Hoeffding-type 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 | ||
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Record in the Search Index
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| dewey-hundreds | 500 - Natural sciences and mathematics |
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| discipline | Mathematik |
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| format | Electronic eBook |
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| id | DE-604.BV042419758 |
| illustrated | Not Illustrated |
| indexdate | 2024-12-20T17:10:41Z |
| institution | BVB |
| isbn | 9781461211280 9781461270171 |
| issn | 0072-5285 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027855175 |
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| physical | 1 Online-Ressource (X, 292 p) |
| psigel | ZDB-2-SMA ZDB-2-BAE ZDB-2-SMA_Archive |
| publishDate | 1984 |
| publishDateSearch | 1984 |
| publishDateSort | 1984 |
| publisher | Springer New York |
| record_format | marc |
| series2 | Graduate Texts in Mathematics |
| spellingShingle | Berg, Christian Harmonic Analysis on Semigroups Theory of Positive Definite and Related Functions Mathematics Topological Groups Topological Groups, Lie Groups Mathematik Harmonische Analyse (DE-588)4023453-8 gnd Halbgruppe (DE-588)4022990-7 gnd |
| subject_GND | (DE-588)4023453-8 (DE-588)4022990-7 |
| title | Harmonic Analysis on Semigroups Theory of Positive Definite and Related Functions |
| title_auth | Harmonic Analysis on Semigroups Theory of Positive Definite and Related Functions |
| title_exact_search | Harmonic Analysis on Semigroups Theory of Positive Definite and Related Functions |
| title_full | Harmonic Analysis on Semigroups Theory of Positive Definite and Related Functions by Christian Berg, Jens Peter Reus Christensen, Paul Ressel |
| title_fullStr | Harmonic Analysis on Semigroups Theory of Positive Definite and Related Functions by Christian Berg, Jens Peter Reus Christensen, Paul Ressel |
| title_full_unstemmed | Harmonic Analysis on Semigroups Theory of Positive Definite and Related Functions by Christian Berg, Jens Peter Reus Christensen, Paul Ressel |
| title_short | Harmonic Analysis on Semigroups |
| title_sort | harmonic analysis on semigroups theory of positive definite and related functions |
| title_sub | Theory of Positive Definite and Related Functions |
| topic | Mathematics Topological Groups Topological Groups, Lie Groups Mathematik Harmonische Analyse (DE-588)4023453-8 gnd Halbgruppe (DE-588)4022990-7 gnd |
| topic_facet | Mathematics Topological Groups Topological Groups, Lie Groups Mathematik Harmonische Analyse Halbgruppe |
| url | https://doi.org/10.1007/978-1-4612-1128-0 |
| work_keys_str_mv | AT bergchristian harmonicanalysisonsemigroupstheoryofpositivedefiniteandrelatedfunctions AT christensenjenspeterreus harmonicanalysisonsemigroupstheoryofpositivedefiniteandrelatedfunctions AT resselpaul harmonicanalysisonsemigroupstheoryofpositivedefiniteandrelatedfunctions |