Harmonic Analysis On Semigroups

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Harmonic Analysis On Semigroups

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Author : C. van den Berg
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Harmonic Analysis On Semigroups written by C. van den Berg and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

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.

Harmonic Analysis On Semigroups

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Author : Christian Berg
language : en
Publisher:
Release Date : 1984

Harmonic Analysis On Semigroups written by Christian Berg and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1984 with Analyse harmonique categories.

Pseudo Differential Operators Markov Processes Fourier Analysis And Semigroups

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Author : Niels Jacob
language : en
Publisher: World Scientific
Release Date : 2001

Pseudo Differential Operators Markov Processes Fourier Analysis And Semigroups written by Niels Jacob and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with Mathematics categories.

This work covers two topics in detail: Fourier analysis, with emphasis on positivity and also on some function spaces and multiplier theorems; and one-parameter operator semigroups with emphasis on Feller semigroups and Lp-sub-Markovian semigroups. In addition, Dirichlet forms are treated.

Operator Semigroups Meet Complex Analysis Harmonic Analysis And Mathematical Physics

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Author : Wolfgang Arendt
language : en
Publisher: Birkhäuser
Release Date : 2015-12-10

Operator Semigroups Meet Complex Analysis Harmonic Analysis And Mathematical Physics written by Wolfgang Arendt and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-12-10 with Mathematics categories.

This proceedings volume originates from a conference held in Herrnhut in June 2013. It provides unique insights into the power of abstract methods and techniques in dealing successfully with numerous applications stemming from classical analysis and mathematical physics. The book features diverse topics in the area of operator semigroups, including partial differential equations, martingale and Hilbert transforms, Banach and von Neumann algebras, Schrödinger operators, maximal regularity and Fourier multipliers, interpolation, operator-theoretical problems (concerning generation, perturbation and dilation, for example), and various qualitative and quantitative Tauberian theorems with a focus on transfinite induction and magics of Cantor. The last fifteen years have seen the dawn of a new era for semigroup theory with the emphasis on applications of abstract results, often unexpected and far removed from traditional ones. The aim of the conference was to bring together prominent experts in the field of modern semigroup theory, harmonic analysis, complex analysis and mathematical physics, and to present the lively interactions between all of those areas and beyond. In addition, the meeting honored the sixtieth anniversary of Prof C. J. K. Batty, whose scientific achievements are an impressive illustration of the conference goal. These proceedings present contributions by prominent scientists at this international conference, which became a landmark event. They will be a valuable and inspiring source of information for graduate students and established researchers.

Harmonic Analysis On Semigroups

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Author : G. Little (Ph.D.)
language : en
Publisher:
Release Date : 1969

Harmonic Analysis On Semigroups written by G. Little (Ph.D.) and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1969 with Harmonic analysis categories.

Pseudo Differential Operators And Markov Processes Volume I Fourier Analysis And Semigroups

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Author : Niels Jacob
language : en
Publisher: World Scientific
Release Date : 2001-11-28

Pseudo Differential Operators And Markov Processes Volume I Fourier Analysis And Semigroups written by Niels Jacob and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-11-28 with Mathematics categories.

After recalling essentials of analysis — including functional analysis, convexity, distribution theory and interpolation theory — this book handles two topics in detail: Fourier analysis, with emphasis on positivity and also on some function spaces and multiplier theorems; and one-parameter operator semigroups with emphasis on Feller semigroups and Lp-sub-Markovian semigroups. In addition, Dirichlet forms are treated. The book is self-contained and offers new material originated by the author and his students./a

Semigroups In Algebra Geometry And Analysis

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Author : Karl H. Hofmann
language : en
Publisher: Walter de Gruyter
Release Date : 2011-06-24

Semigroups In Algebra Geometry And Analysis written by Karl H. Hofmann and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-06-24 with Mathematics categories.

The aim of the series is to present new and important developments in pure and applied mathematics. Well established in the community over two decades, it offers a large library of mathematics including several important classics. The volumes supply thorough and detailed expositions of the methods and ideas essential to the topics in question. In addition, they convey their relationships to other parts of mathematics. The series is addressed to advanced readers wishing to thoroughly study the topic. Editorial Board Lev Birbrair, Universidade Federal do Ceará, Fortaleza, Brasil Walter D. Neumann, Columbia University, New York, USA Markus J. Pflaum, University of Colorado, Boulder, USA Dierk Schleicher, Jacobs University, Bremen, Germany Katrin Wendland, University of Freiburg, Germany Honorary Editor Victor P. Maslov, Russian Academy of Sciences, Moscow, Russia Titles in planning include Yuri A. Bahturin, Identical Relations in Lie Algebras (2019) Yakov G. Berkovich and Z. Janko, Groups of Prime Power Order, Volume 6 (2019) Yakov G. Berkovich, Lev G. Kazarin, and Emmanuel M. Zhmud', Characters of Finite Groups, Volume 2 (2019) Jorge Herbert Soares de Lira, Variational Problems for Hypersurfaces in Riemannian Manifolds (2019) Volker Mayer, Mariusz Urbański, and Anna Zdunik, Random and Conformal Dynamical Systems (2021) Ioannis Diamantis, Boštjan Gabrovšek, Sofia Lambropoulou, and Maciej Mroczkowski, Knot Theory of Lens Spaces (2021)

Theory Of Semigroups And Applications

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Author : Kalyan B. Sinha
language : en
Publisher: Springer
Release Date : 2017-07-12

Theory Of Semigroups And Applications written by Kalyan B. Sinha and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-07-12 with Mathematics categories.

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.

Harmonic Functions On Groups And Fourier Algebras

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Author : Cho-Ho Chu
language : en
Publisher: Springer
Release Date : 2004-10-11

Harmonic Functions On Groups And Fourier Algebras written by Cho-Ho Chu and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-10-11 with Mathematics categories.

This research monograph introduces some new aspects to the theory of harmonic functions and related topics. The authors study the analytic algebraic structures of the space of bounded harmonic functions on locally compact groups and its non-commutative analogue, the space of harmonic functionals on Fourier algebras. Both spaces are shown to be the range of a contractive projection on a von Neumann algebra and therefore admit Jordan algebraic structures. This provides a natural setting to apply recent results from non-associative analysis, semigroups and Fourier algebras. Topics discussed include Poisson representations, Poisson spaces, quotients of Fourier algebras and the Murray-von Neumann classification of harmonic functionals.

Analysis On Semigroups

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Author : John F. Berglund
language : en
Publisher: Wiley-Interscience
Release Date : 1989

Analysis On Semigroups written by John F. Berglund and has been published by Wiley-Interscience this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989 with Mathematics categories.

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.