Harmonic Analysis on Semigroups: Theory of Positive Definite and Related Functions

Berg, Christian, and Berg, C, and Christensen, J P R

ISBN 10: 0387909257 / ISBN 13: 9780387909257

Published by Springer, New York, NY, 1984

About this Item

***INTERNATIONAL EDITION*** Read carefully before purchase: This book is the international edition in mint condition with the different ISBN and book cover design, the major content is printed in full English as same as the original North American edition. The book printed in black and white, generally send in twenty-four hours after the order confirmed. All shipments contain tracking numbers. Great professional textbook selling experience and expedite shipping service. Sewn binding. Cloth over boards. 302 p. Contains: Illustrations. Applied Mathematical Sciences, 100. Audience: General/trade.

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Bibliographic Details

• Title: Harmonic Analysis on Semigroups: Theory of Positive Definite and Related Functions
• Publisher: Springer, New York, NY
• Publication Date: 1984
• Language: English
• ISBN 10: 0387909257
• ISBN 13: 9780387909257
• Binding: Trade paperback
• Edition: First edition.
• Condition: New in new dust jacket.

About this title

Synopsis

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.