Harmonic Analysis On Semigroups

Author : C. van den Berg,J. P. R. Christensen,P. Ressel
Publisher : Springer Science & Business Media
Page : 299 pages
File Size : 43,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461211280

Get Book

Harmonic Analysis on Semigroups by C. van den Berg,J. P. R. Christensen,P. Ressel Pdf

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.

Author : Christian Berg,Jens Peter Reus Christensen,Paul Ressel
Publisher : Unknown
Page : 289 pages
File Size : 42,9 Mb
Release : 1984
Category : Analyse harmonique
ISBN : 3540909257

Get Book

Harmonic Analysis on Semigroups by Christian Berg,Jens Peter Reus Christensen,Paul Ressel Pdf

Author : Charles F. Dunkl,Donald E. Ramirez
Publisher : Unknown
Page : 184 pages
File Size : 43,6 Mb
Release : 1971
Category : Mathematics
ISBN : UCAL:B4980178

Get Book

Topics in Harmonic Analysis by Charles F. Dunkl,Donald E. Ramirez Pdf

Author : Niels Jacob
Publisher : World Scientific
Page : 517 pages
File Size : 49,6 Mb
Release : 2001-11-28
Category : Mathematics
ISBN : 9781783261345

Get Book

Pseudo Differential Operators And Markov Processes, Volume I: Fourier Analysis And Semigroups by Niels Jacob Pdf

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

Author : Wolfgang Arendt,Ralph Chill,Yuri Tomilov
Publisher : Birkhäuser
Page : 496 pages
File Size : 53,6 Mb
Release : 2015-12-10
Category : Mathematics
ISBN : 9783319184944

Get Book

Operator Semigroups Meet Complex Analysis, Harmonic Analysis and Mathematical Physics by Wolfgang Arendt,Ralph Chill,Yuri Tomilov Pdf

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.

Author : Elias M. Stein
Publisher : Princeton University Press
Page : 168 pages
File Size : 49,5 Mb
Release : 1970-02-21
Category : Mathematics
ISBN : 0691080674

Get Book

Topics in Harmonic Analysis, Related to the Littlewood-Paley Theory by Elias M. Stein Pdf

This work deals with an extension of the classical Littlewood-Paley theory in the context of symmetric diffusion semigroups. In this general setting there are applications to a variety of problems, such as those arising in the study of the expansions coming from second order elliptic operators. A review of background material in Lie groups and martingale theory is included to make the monograph more accessible to the student.

Author : Elias M. Stein
Publisher : Princeton University Press
Page : 160 pages
File Size : 54,7 Mb
Release : 2016-03-02
Category : Mathematics
ISBN : 9781400881871

Get Book

Topics in Harmonic Analysis Related to the Littlewood-Paley Theory. (AM-63), Volume 63 by Elias M. Stein Pdf

This work deals with an extension of the classical Littlewood-Paley theory in the context of symmetric diffusion semigroups. In this general setting there are applications to a variety of problems, such as those arising in the study of the expansions coming from second order elliptic operators. A review of background material in Lie groups and martingale theory is included to make the monograph more accessible to the student.

Author : Walter R. Bloom,Herbert Heyer
Publisher : Walter de Gruyter
Page : 609 pages
File Size : 53,7 Mb
Release : 2011-04-20
Category : Mathematics
ISBN : 9783110877595

Get Book

Harmonic Analysis of Probability Measures on Hypergroups by Walter R. Bloom,Herbert Heyer Pdf

The series is devoted to the publication of monographs and high-level textbooks in mathematics, mathematical methods and their applications. Apart from covering important areas of current interest, a major aim is to make topics of an interdisciplinary nature accessible to the non-specialist. The works in this series are addressed to advanced students and researchers in mathematics and theoretical physics. In addition, it can serve as a guide for lectures and seminars on a graduate level. The series de Gruyter Studies in Mathematics was founded ca. 30 years ago by the late Professor Heinz Bauer and Professor Peter Gabriel with the aim to establish a series of monographs and textbooks of high standard, written by scholars with an international reputation presenting current fields of research in pure and applied mathematics. While the editorial board of the Studies has changed with the years, the aspirations of the Studies are unchanged. In times of rapid growth of mathematical knowledge carefully written monographs and textbooks written by experts are needed more than ever, not least to pave the way for the next generation of mathematicians. In this sense the editorial board and the publisher of the Studies are devoted to continue the Studies as a service to the mathematical community. Please submit any book proposals to Niels Jacob.

Author : Niels Jacob
Publisher : World Scientific
Page : 517 pages
File Size : 40,9 Mb
Release : 2001
Category : Mathematics
ISBN : 9781860942938

Get Book

Pseudo Differential Operators & Markov Processes: Fourier analysis and semigroups by Niels Jacob Pdf

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.

Author : Einar Hille,Ralph Saul Phillips
Publisher : American Mathematical Soc.
Page : 808 pages
File Size : 48,9 Mb
Release : 1996-02-06
Category : Banach algebras
ISBN : 9780821810316

Get Book

Functional Analysis and Semi-groups by Einar Hille,Ralph Saul Phillips Pdf

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.

Author : Kalyan B. Sinha,Sachi Srivastava
Publisher : Springer
Page : 169 pages
File Size : 46,8 Mb
Release : 2017-07-12
Category : Mathematics
ISBN : 9789811048647

Get Book

Theory of Semigroups and Applications by Kalyan B. Sinha,Sachi Srivastava Pdf

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.

Author : Cho-Ho Chu,Anthony To-Ming Lau
Publisher : Springer
Page : 100 pages
File Size : 41,8 Mb
Release : 2004-10-11
Category : Mathematics
ISBN : 9783540477938

Get Book

Harmonic Functions on Groups and Fourier Algebras by Cho-Ho Chu,Anthony To-Ming Lau Pdf

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.

Author : Niels Jacob
Publisher : World Scientific
Page : 528 pages
File Size : 40,8 Mb
Release : 2001
Category : Mathematics
ISBN : 1860949746

Get Book

Pseudo Differential Operators and Markov Processes by Niels Jacob Pdf

After recalling essentials of analysis OCo including functional analysis, convexity, distribution theory and interpolation theory OCo 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. Sample Chapter(s). Introduction: Pseudo Differential Operators and Markov Processes (207 KB). Chapter 1: Introduction (190 KB). Contents: Essentials from Analysis: Calculus Results; Convexity; Some Interpolation Theory; Fourier Analysis and Convolution Semigroups: The PaleyOCoWienerOCoSchwartz Theorem; Bounded Borel Measures and Positive Definite Functions; Convolution Semigroups and Negative Definite Functions; The L(r)vyOCoKhinchin Formula for Continuous Negative Definite Functions; Bernstein Functions and Subordination of Convolution Semigroups; Fourier Multiplier Theorems; One Parameter Semigroups: Strongly Continuous Operator Semigroups; Subordination in the Sense of Bochner for Operator Semigroups; Generators of Feller Semigroups; Dirichlet Forms and Generators of Sub-Markovian Semigroups; and other papers. Readership: Graduate students, researchers and lecturers in analysis & differential equations, stochastics, probability & statistics, and mathematical physics."

Author : Karl H. Hofmann,Jimmie D. Lawson,Ernest B. Vinberg
Publisher : Walter de Gruyter
Page : 385 pages
File Size : 43,5 Mb
Release : 2011-06-24
Category : Mathematics
ISBN : 9783110885583

Get Book

Semigroups in Algebra, Geometry and Analysis by Karl H. Hofmann,Jimmie D. Lawson,Ernest B. Vinberg Pdf

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)

Author : John F. Berglund,Hugo D. Junghenn,Paul Milnes
Publisher : Wiley-Interscience
Page : 360 pages
File Size : 48,8 Mb
Release : 1989
Category : Mathematics
ISBN : UCAL:B5008603

Get Book

Analysis on Semigroups by John F. Berglund,Hugo D. Junghenn,Paul Milnes Pdf

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.