Download EBOOK Harmonic Analysis on Semigroups: Theory of Positive Definite and Related Functions PDF for free
 
Category: Science & Geography
The author of the book: Christian Berg
Format files: PDF, EPUB, TXT, DOCX
The size of the: 798 KB
Language: English
ISBN13: 9780387909257
Edition: SpringerVerlag New York Inc.
Date of issue: 6 June 1984

Description of the book "Harmonic Analysis on Semigroups: Theory of Positive Definite and Related Functions":
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" is positive definite for all finite choices of elements St, ..., Sn from S. The three basic results PDF 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 ePub which occurs in mathematics as often as the notion of a Hilbert space.
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Christian Berg
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