Harmonic Analysis Of Probability Measures On Hypergroups

Author : Walter R. Bloom,Herbert Heyer
Publisher : Walter de Gruyter
Page : 609 pages
File Size : 43,5 Mb
Release : 2011-04-20
Category : Mathematics
ISBN : 9783110877595

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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 : H. Heyer
Publisher : Springer Science & Business Media
Page : 491 pages
File Size : 43,9 Mb
Release : 2013-11-11
Category : Mathematics
ISBN : 9781489923646

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Probability Measures on Groups X by H. Heyer Pdf

The present volume contains the transactions of the lOth Oberwolfach Conference on "Probability Measures on Groups". The series of these meetings inaugurated in 1970 by L. Schmetterer and the editor is devoted to an intensive exchange of ideas on a subject which developed from the relations between various topics of mathematics: measure theory, probability theory, group theory, harmonic analysis, special functions, partial differential operators, quantum stochastics, just to name the most significant ones. Over the years the fruitful interplay broadened in various directions: new group-related structures such as convolution algebras, generalized translation spaces, hypercomplex systems, and hypergroups arose from generalizations as well as from applications, and a gradual refinement of the combinatorial, Banach-algebraic and Fourier analytic methods led to more precise insights into the theory. In a period of highest specialization in scientific thought the separated minds should be reunited by actively emphasizing similarities, analogies and coincidences between ideas in their fields of research. Although there is no real separation between one field and another - David Hilbert denied even the existence of any difference between pure and applied mathematics - bridges between probability theory on one side and algebra, topology and geometry on the other side remain absolutely necessary. They provide a favorable ground for the communication between apparently disjoint research groups and motivate the framework of what is nowadays called "Structural probability theory".

Author : Ken Ross
Publisher : Springer Science & Business Media
Page : 248 pages
File Size : 51,8 Mb
Release : 2013-11-11
Category : Mathematics
ISBN : 9780817643485

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Harmonic Analysis and Hypergroups by Ken Ross Pdf

An underlying theme in this text is the notion of hypergroups, the theory of which has been developed and used in fields as diverse as special functions, differential equations, probability theory, representation theory, measure theory, Hopf algebras, and quantum groups. Other topics include the harmonic analysis of analytic functions, ergodic theory and wavelets.

Author : Herbert Heyer,Gyula Pap
Publisher : World Scientific
Page : 425 pages
File Size : 48,8 Mb
Release : 2010
Category : Mathematics
ISBN : 9789814282482

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Structural Aspects in the Theory of Probability by Herbert Heyer,Gyula Pap Pdf

The book is conceived as a text accompanying the traditional graduate courses on probability theory. An important feature of this enlarged version is the emphasis on algebraic-topological aspects leading to a wider and deeper understanding of basic theorems such as those on the structure of continuous convolution semigroups and the corresponding processes with independent increments. Fourier transformation ? the method applied within the settings of Banach spaces, locally compact Abelian groups and commutative hypergroups ? is given an in-depth discussion. This powerful analytic tool along with the relevant facts of harmonic analysis make it possible to study certain properties of stochastic processes in dependence of the algebraic-topological structure of their state spaces. In extension of the first edition, the new edition contains chapters on the probability theory of generalized convolution structures such as polynomial and Sturm?Liouville hypergroups, and on the central limit problem for groups such as tori, p-adic groups and solenoids.

Author : H. Heyer
Publisher : Springer
Page : 520 pages
File Size : 46,7 Mb
Release : 1992-02-29
Category : Mathematics
ISBN : 0306440598

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Probability Measures on Groups X by H. Heyer Pdf

The present volume contains the transactions of the lOth Oberwolfach Conference on "Probability Measures on Groups". The series of these meetings inaugurated in 1970 by L. Schmetterer and the editor is devoted to an intensive exchange of ideas on a subject which developed from the relations between various topics of mathematics: measure theory, probability theory, group theory, harmonic analysis, special functions, partial differential operators, quantum stochastics, just to name the most significant ones. Over the years the fruitful interplay broadened in various directions: new group-related structures such as convolution algebras, generalized translation spaces, hypercomplex systems, and hypergroups arose from generalizations as well as from applications, and a gradual refinement of the combinatorial, Banach-algebraic and Fourier analytic methods led to more precise insights into the theory. In a period of highest specialization in scientific thought the separated minds should be reunited by actively emphasizing similarities, analogies and coincidences between ideas in their fields of research. Although there is no real separation between one field and another - David Hilbert denied even the existence of any difference between pure and applied mathematics - bridges between probability theory on one side and algebra, topology and geometry on the other side remain absolutely necessary. They provide a favorable ground for the communication between apparently disjoint research groups and motivate the framework of what is nowadays called "Structural probability theory".

Author : Anonim
Publisher : American Mathematical Soc.
Page : 458 pages
File Size : 48,5 Mb
Release : 1995-02-28
Category : Mathematics
ISBN : 9780821802977

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Applications of Hypergroups and Related Measure Algebras by Anonim Pdf

`The most important single thing about this conference was that it brought together for the first time representatives of all major groups of users of hypergroups. [They] talked to each other about how they were using hypergroups in fields as diverse as special functions, probability theory, representation theory, measure algebras, Hopf algebras, and Hecke algebras. This led to fireworks.' - from the Introduction. Hypergroups occur in a wide variety of contexts, and mathematicians the world over have been discovering this same mathematical structure hidden in very different applications. The diverse viewpoints on the subject have led to the need for a common perspective, if not a common theory. Presenting the proceedings of a Joint Summer Research Conference held in Seattle in the summer of 1993, this book will serve as a valuable starting point and reference tool for the wide range of users of hypergroups and make it easier for an even larger audience to use these structures in their work.

Author : Rupert Lasser
Publisher : World Scientific
Page : 621 pages
File Size : 40,9 Mb
Release : 2022-12-06
Category : Mathematics
ISBN : 9789811266218

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Harmonic Analysis On Hypergroups: Approximation And Stochastic Sequences by Rupert Lasser Pdf

The book aims at giving a monographic presentation of the abstract harmonic analysis of hypergroups, while combining it with applied topics of spectral analysis, approximation by orthogonal expansions and stochastic sequences. Hypergroups are locally compact Hausdorff spaces equipped with a convolution, an involution and a unit element. Related algebraic structures had already been studied by Frobenius around 1900. Their axiomatic characterisation in harmonic analysis was later developed in the 1970s. Hypergoups naturally emerge in seemingly different application areas as time series analysis, probability theory and theoretical physics.The book presents harmonic analysis on commutative and polynomial hypergroups as well as weakly stationary random fields and sequences thereon. For polynomial hypergroups also difference equations and stationary sequences are considered. At greater extent than in the existing literature, the book compiles a rather comprehensive list of hypergroups, in particular of polynomial hypergroups. With an eye on readers at advanced undergraduate and graduate level, the proofs are generally worked out in careful detail. The bibliography is extensive.

Author : László Székelyhidi
Publisher : World Scientific
Page : 210 pages
File Size : 53,5 Mb
Release : 2013
Category : Mathematics
ISBN : 9789814407007

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Functional Equations on Hypergroups by László Székelyhidi Pdf

The theory of hypergroups is a rapidly developing area of mathematics due to its diverse applications in different areas like probability, harmonic analysis, etc. This book exhibits the use of functional equations and spectral synthesis in the theory of hypergroups. It also presents the fruitful consequences of this delicate "marriage" where the methods of spectral analysis and synthesis can provide an efficient tool in characterization problems of function classes on hypergroups. This book is written for the interested reader who has open eyes for both functional equations and hypergroups, and who dares to enter a new world of ideas, a new world of methods - and, sometimes, a new world of unexpected difficulties.

Author : H. Heyer
Publisher : Springer Science & Business Media
Page : 542 pages
File Size : 50,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642667060

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Probability Measures on Locally Compact Groups by H. Heyer Pdf

Probability measures on algebraic-topological structures such as topological semi groups, groups, and vector spaces have become of increasing importance in recent years for probabilists interested in the structural aspects of the theory as well as for analysts aiming at applications within the scope of probability theory. In order to obtain a natural framework for a first systematic presentation of the most developed part of the work done in the field we restrict ourselves to prob ability measures on locally compact groups. At the same time we stress the non Abelian aspect. Thus the book is concerned with a set of problems which can be regarded either from the probabilistic or from the harmonic-analytic point of view. In fact, it seems to be the synthesis of these two viewpoints, the initial inspiration coming from probability and the refined techniques from harmonic analysis which made this newly established subject so fascinating. The goal of the presentation is to give a fairly complete treatment of the central limit problem for probability measures on a locally compact group. In analogy to the classical theory the discussion is centered around the infinitely divisible probability measures on the group and their relationship to the convergence of infinitesimal triangular systems.

Author : Joachim Hilgert
Publisher : World Scientific
Page : 337 pages
File Size : 53,8 Mb
Release : 2009
Category : Mathematics
ISBN : 9789812832818

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Proceedings of the Fourth German-Japanese Symposium, Infinite Dimensional Harmonic Analysis IV by Joachim Hilgert Pdf

The Fourth Conference on Infinite Dimensional Harmonic Analysis brought together experts in harmonic analysis, operator algebras and probability theory. Most of the articles deal with the limit behavior of systems with many degrees of freedom in the presence of symmetry constraints. This volume gives new directions in research bringing together probability theory and representation theory.

Author : Anonim
Publisher : Unknown
Page : 128 pages
File Size : 44,8 Mb
Release : 2024-07-03
Category : Electronic
ISBN : 9789814470445

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Infinite Dimensional Harmonic Analysis IV by Anonim Pdf

Author : Herbert Heyer
Publisher : Lecture Notes in Mathematics
Page : 452 pages
File Size : 44,8 Mb
Release : 1989-07-12
Category : Mathematics
ISBN : UCSD:31822026303750

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Probability Measures on Groups IX by Herbert Heyer Pdf

The latest in this series of Oberwolfach conferences focussed on the interplay between structural probability theory and various other areas of pure and applied mathematics such as Tauberian theory, infinite-dimensional rotation groups, central limit theorems, harmonizable processes, and spherical data. Thus it was attended by mathematicians whose research interests range from number theory to quantum physics in conjunction with structural properties of probabilistic phenomena. This volume contains 5 survey articles submitted on special invitation and 25 original research papers.

Author : Gregory Budzban,Arunava Mukherjea
Publisher : American Mathematical Soc.
Page : 250 pages
File Size : 41,8 Mb
Release : 2000
Category : Mathematics
ISBN : 9780821820278

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Probability on Algebraic Structures by Gregory Budzban,Arunava Mukherjea Pdf

This volume presents results from an AMS Special Session held on the topic in Gainesville (FL). Papers included are written by an international group of well-known specialists who offer an important cross-section of current work in the field. In addition there are two expository papers that provide an avenue for non-specialists to comprehend problems in this area. The breadth of research in this area is evident by the variety of articles presented in the volume. Results concern probability on Lie groups and general locally compact groups. Generalizations of groups appear as hypergroups, abstract semigroups, and semigroups of matrices. Work on symmetric cones is included. Lastly, there are a number of articles on the current progress in constructing stochastic processes on quantum groups.

Author : Anonim
Publisher : Unknown
Page : 128 pages
File Size : 49,8 Mb
Release : 2024-07-03
Category : Electronic
ISBN : 9789814466943

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Structural Aspects in the Theory of Probability by Anonim Pdf

Author : Anthony To-Ming Lau,Volker Runde
Publisher : American Mathematical Soc.
Page : 362 pages
File Size : 41,8 Mb
Release : 2004
Category : Mathematics
ISBN : 9780821834718

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Banach Algebras and Their Applications by Anthony To-Ming Lau,Volker Runde Pdf

This proceedings volume is from the international conference on Banach Algebras and Their Applications held at the University of Alberta (Edmonton). It contains a collection of refereed research papers and high-level expository articles that offer a panorama of Banach algebra theory and its manifold applications. Topics in the book range from - theory to abstract harmonic analysis to operator theory. It is suitable for graduate students and researchers interested in Banach algebras.