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Harmonic Analysis on Semigroups

2012-12-06 Mathematics
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Release : 2012-12-06
Genre : Mathematics
Kind : eBook
Book Rating : 28X/5 ( reviews)

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Book Synopsis Harmonic Analysis on Semigroups by : C. van den Berg

Download or read book Harmonic Analysis on Semigroups written by C. van den Berg. This book was released on 2012-12-06. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Analysis on Semigroups

1989 Mathematics
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Release : 1989
Genre : Mathematics
Kind : eBook
Book Rating : /5 ( reviews)

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Book Synopsis Analysis on Semigroups by : John F. Berglund

Download or read book Analysis on Semigroups written by John F. Berglund. This book was released on 1989. Available in PDF, EPUB and Kindle. Book excerpt: This treatment of analysis on semigroups stresses the functional analytical and dynamical theory of continuous representations of semitopological semigroups. Topics covered include compact semitopological semigroups, invariant means and idempotent means on compact semitopological semigroups, affine compactifications, left multiplicatively continuous functions and weakly left continuous functions, compactifications of infinite direct products, and weakly almost periodic semigroups of Markov operators. Contains over 200 exercises, from simple applications and examples to further developments of the theory.

Functional Analysis and Semi-groups

1996-02-06 Mathematics
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Release : 1996-02-06
Genre : Mathematics
Kind : eBook
Book Rating : 316/5 ( reviews)

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Book Synopsis Functional Analysis and Semi-groups by : Einar Hille

Download or read book Functional Analysis and Semi-groups written by Einar Hille. This book was released on 1996-02-06. Available in PDF, EPUB and Kindle. Book excerpt: Early in 1952 it became obvious that a new printing would be needed, and new advances in the theory called for extensive revision. It has been completely rewritten, mostly by Phillips, and much has been added while keeping the existing framework. Thus, the algebraic tools play a major role, and are introduced early, leading to a more satisfactory operational calculus and spectral theory. The Laplace-Stieltjes transform methods, used by Hille, have not been replaced but rather supplemented by the new tools. - Foreword.

Semigroups of Linear Operators

2019-08-15 Mathematics
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Release : 2019-08-15
Genre : Mathematics
Kind : eBook
Book Rating : 097/5 ( reviews)

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Book Synopsis Semigroups of Linear Operators by : David Applebaum

Download or read book Semigroups of Linear Operators written by David Applebaum. This book was released on 2019-08-15. Available in PDF, EPUB and Kindle. Book excerpt: Provides a graduate-level introduction to the theory of semigroups of operators.

Theory of Semigroups and Applications

2017-07-12 Mathematics
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Release : 2017-07-12
Genre : Mathematics
Kind : eBook
Book Rating : 649/5 ( reviews)

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Book Synopsis Theory of Semigroups and Applications by : Kalyan B. Sinha

Download or read book Theory of Semigroups and Applications written by Kalyan B. Sinha. This book was released on 2017-07-12. Available in PDF, EPUB and Kindle. Book excerpt: The book presents major topics in semigroups, such as operator theory, partial differential equations, harmonic analysis, probability and statistics and classical and quantum mechanics, and applications. Along with a systematic development of the subject, the book emphasises on the explorations of the contact areas and interfaces, supported by the presentations of explicit computations, wherever feasible. Designed into seven chapters and three appendixes, the book targets to the graduate and senior undergraduate students of mathematics, as well as researchers in the respective areas. The book envisages the pre-requisites of a good understanding of real analysis with elements of the theory of measures and integration, and a first course in functional analysis and in the theory of operators. Chapters 4 through 6 contain advanced topics, which have many interesting applications such as the Feynman–Kac formula, the central limit theorem and the construction of Markov semigroups. Many examples have been given in each chapter, partly to initiate and motivate the theory developed and partly to underscore the applications. The choice of topics in this vastly developed book is a difficult one, and the authors have made an effort to stay closer to applications instead of bringing in too many abstract concepts.

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