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Harmonic Analysis on Semigroups by C. Van Den Berg Hardcover | Indigo Chapters
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Harmonic Analysis on Semigroups by C. Van Den Berg Hardcover | Indigo Chapters - new book

ISBN: 9780387909257

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… More...

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Berg, Christian and Jens Peter Reus Christensen and Paul Ressel:

HARMONIC ANALYSIS ON SEMIGROUPS: THEORY OF POSITIVE DEFINITE AND RELATED FUNCTIONS Graduate Texts in Mathematics 100 - hardcover

1984, ISBN: 9780387909257

New York, NY: Springer-Verlag, 1984. Hardcover. Very good/No jacket issued. Graduate Texts in Mathematics 100. New York, NY: Springer-Verlag, 1984. With 3 Illustrations. 289 pp. Har… More...

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Harmonic Analysis on Semigroups - C. van den Berg J. P. R. Christensen P. Ressel
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C. van den Berg J. P. R. Christensen P. Ressel:
Harmonic Analysis on Semigroups - hardcover

1984

ISBN: 9780387909257

[ED: Gebunden], [PU: Springer New York], Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. The Fourier transform and the Laplace transform o… More...

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Van Den Berg, C.:
Harmonic Analysis on Semigroups: Theory of Positive Definite and Related Functions (Graduate Texts in Mathematics, 100) - hardcover

1984, ISBN: 9780387909257

hardcover, Access codes and supplements are not guaranteed with used items. May be an ex-library book., Gebraucht, guter Zustand, [PU: Springer]

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C. van den Berg; J. P. R. Christensen; P. Ressel:
Harmonic Analysis on Semigroups: Theory of Positive Definite and Related Functions (Graduate Texts in Mathematics) (v. 100) - hardcover

1984, ISBN: 9780387909257

Springer, 1984-06-06. Hardcover. Good., Springer, 1984-06-06, 2.5

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Harmonic Analysis on Semigroups by C. Van Den Berg Hardcover | Indigo Chapters
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ISBN:

0387909257


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.

Details of the book - Harmonic Analysis on Semigroups by C. Van Den Berg Hardcover | Indigo Chapters


EAN (ISBN-13): 9780387909257
ISBN (ISBN-10): 0387909257
Hardcover
Paperback
Publishing year: 1984
Publisher: C. Van Den Berg

Book in our database since 2007-05-26T14:46:43-04:00 (New York)
Detail page last modified on 2023-03-30T03:44:19-04:00 (New York)
ISBN/EAN: 0387909257

ISBN - alternate spelling:
0-387-90925-7, 978-0-387-90925-7
Alternate spelling and related search-keywords:
Book author: berg christian, ressel peter, van den berg, christensen, ress, christ, reuß christian, jens christian, christen christian, jens peter paul
Book title: positive definite, harmonic analysis semigroups, semigroups and, ressel, think positive, the theory functions, graduate texts mathematics

Information from Publisher

Author: C. van den Berg; J. P. R. Christensen; P. Ressel
Title: Graduate Texts in Mathematics; Harmonic Analysis on Semigroups - Theory of Positive Definite and Related Functions
Publisher: Springer; Springer US
292 Pages
Publishing year: 1984-06-06
New York; NY; US
Language: English
53,49 € (DE)
54,99 € (AT)
59,00 CHF (CH)
Available
X, 292 p.

BB; Hardcover, Softcover / Mathematik/Arithmetik, Algebra; Gruppen und Gruppentheorie; Verstehen; Fourier transform; Functions; Halbgruppe; Harmonische Analyse; Hilbert space; Positiv definite Funktion; Vector space; harmonic analysis; Topological Groups and Lie Groups; BC

1 Introduction to Locally Convex Topological Vector Spaces and Dual Pairs.- §1. Locally Convex Vector Spaces.- §2. Hahn-Banach Theorems.- §3. Dual Pairs.- Notes and Remarks.- 2 Radon Measures and Integral Representations.- §1. Introduction to Radon Measures on Hausdorff Spaces.- §2. The Riesz Representation Theorem.- §3. Weak Convergence of Finite Radon Measures.- §4. Vague Convergence of Radon Measures on Locally Compact Spaces.- §5. Introduction to the Theory of Integral Representations.- Notes and Remarks.- 3 General Results on Positive and Negative Definite Matrices and Kernels.- §1. Definitions and Some Simple Properties of Positive and Negative Definite Kernels.- §2. Relations Between Positive and Negative Definite Kernels.- §3. Hubert Space Representation of Positive and Negative Definite Kernels.- Notes and Remarks.- 4 Main Results on Positive and Negative Definite Functions on Semigroups.- §1. Definitions and Simple Properties 86 §2. Exponentially Bounded Positive Definite Functions on Abelian Semigroups.- §3. Negative Definite Functions on Abelian Semigroups.- §4. Examples of Positive and Negative Definite Functions.- §5. T-Positive Functions.- §6. Completely Monotone and Alternating Functions.- Notes and Remarks.- 5 Schoenberg-Type Results for Positive and Negative Definite Functions.- §1. Schoenberg Triples.- §2. Norm Dependent Positive Definite Functions on Banach Spaces.- §3. Functions Operating on Positive Definite Matrices.- §4. Schoenberg’s Theorem for the Complex Hilbert Sphere.- §5. The Real Infinite Dimensional Hyperbolic Space.- Notes and Remarks.- 6 Positive Definite Functions and Moment Functions.- §1. Moment Functions.- §2. The One-Dimensional Moment Problem.- §3. The Multi-Dimensional Moment Problem.- §4. TheTwo-Sided Moment Problem.- §5. Perfect Semigroups.- Notes and Remarks.- 7 Hoeffding’s Inequality and Multivariate Majorization.- §1. The Discrete Case.- §2. Extension to Nondiscrete Semigroups.- §3. Completely Negative Definite Functions and Schur-Monotonicity.- Notes and Remarks.- 8 Positive and Negative Definite Functions on Abelian Semigroups Without Zero.- §1. Quasibounded Positive and Negative Definite Functions.- §2. Completely Monotone and Completely Alternating Functions.- Notes and Remarks.- References.- List of Symbols.

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