Harmonic Functions On Groups And Fourier Algebras

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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.

Harmonic Functions On Groups And Fourier Algebras

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Author : Cho-Ho Chu
language : en
Publisher:
Release Date : 2014-01-15

Harmonic Functions On Groups And Fourier Algebras written by Cho-Ho Chu and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-15 with categories.

Fourier And Fourier Stieltjes Algebras On Locally Compact Groups

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Author : Eberhard Kaniuth
language : en
Publisher: American Mathematical Soc.
Release Date : 2018-07-05

Fourier And Fourier Stieltjes Algebras On Locally Compact Groups written by Eberhard Kaniuth and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-07-05 with Mathematics categories.

The theory of the Fourier algebra lies at the crossroads of several areas of analysis. Its roots are in locally compact groups and group representations, but it requires a considerable amount of functional analysis, mainly Banach algebras. In recent years it has made a major connection to the subject of operator spaces, to the enrichment of both. In this book two leading experts provide a road map to roughly 50 years of research detailing the role that the Fourier and Fourier-Stieltjes algebras have played in not only helping to better understand the nature of locally compact groups, but also in building bridges between abstract harmonic analysis, Banach algebras, and operator algebras. All of the important topics have been included, which makes this book a comprehensive survey of the field as it currently exists. Since the book is, in part, aimed at graduate students, the authors offer complete and readable proofs of all results. The book will be well received by the community in abstract harmonic analysis and will be particularly useful for doctoral and postdoctoral mathematicians conducting research in this important and vibrant area.

Fourier Analysis On Finite Abelian Groups

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Author : Bao Luong
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-08-14

Fourier Analysis On Finite Abelian Groups written by Bao Luong 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 2009-08-14 with Mathematics categories.

This unified, self-contained book examines the mathematical tools used for decomposing and analyzing functions, specifically, the application of the [discrete] Fourier transform to finite Abelian groups. With countless examples and unique exercise sets at the end of each section, Fourier Analysis on Finite Abelian Groups is a perfect companion to a first course in Fourier analysis. This text introduces mathematics students to subjects that are within their reach, but it also has powerful applications that may appeal to advanced researchers and mathematicians. The only prerequisites necessary are group theory, linear algebra, and complex analysis.

Banach Algebras And Their Applications

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Author : Anthony To-Ming Lau
language : en
Publisher: American Mathematical Soc.
Release Date : 2004

Banach Algebras And Their Applications written by Anthony To-Ming Lau and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Mathematics categories.

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.

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 The Heisenberg Group

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Author : Sundaram Thangavelu
language : en
Publisher: Springer Science & Business Media
Release Date : 1998-03-24

Harmonic Analysis On The Heisenberg Group written by Sundaram Thangavelu 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 1998-03-24 with Mathematics categories.

This monograph deals with various aspects of harmonic analysis on the Heisenberg group, which is the most commutative among the non-commutative Lie groups, and, hence gives the greatest opportunity for generalizing the remarkable results of Euclidian harmonic analysis.

Point Estimation Of Root Finding Methods

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Author : Miodrag Petkovic
language : en
Publisher: Springer
Release Date : 2008-05-29

Point Estimation Of Root Finding Methods written by Miodrag Petkovic and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-05-29 with Mathematics categories.

The problem of solving nonlinear equations and systems of equations ranks among the most signi?cant in the theory and practice, not only of applied mathematicsbutalsoofmanybranchesofengineeringsciences,physics,c- puter science, astronomy, ?nance, and so on. A glance at the bibliography and the list of great mathematicians who have worked on this topic points to a high level of contemporary interest. Although the rapid development of digital computers led to the e?ective implementation of many numerical methods, in practical realization, it is necessary to solve various problems such as computational e?ciency based on the total central processor unit time, the construction of iterative methods which possess a fast convergence in the presence of multiplicity (or clusters) of a desired solution, the control of rounding errors, information about error bounds of obtained approximate solution, stating computationally veri?able initial conditions that ensure a safe convergence, etc. It is the solution of these challenging problems that was the principal motivation for the present study. In this book, we are mainly concerned with the statement and study of initial conditions that provide the guaranteed convergence of an iterative method for solving equations of the form f(z) = 0. The traditional approach to this problem is mainly based on asymptotic convergence analysis using some strong hypotheses on di?erentiability and derivative bounds in a rather wide domain.

Symplectic 4 Manifolds And Algebraic Surfaces

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Author : Denis Auroux
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-04-17

Symplectic 4 Manifolds And Algebraic Surfaces written by Denis Auroux 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 2008-04-17 with Mathematics categories.

Modern approaches to the study of symplectic 4-manifolds and algebraic surfaces combine a wide range of techniques and sources of inspiration. Gauge theory, symplectic geometry, pseudoholomorphic curves, singularity theory, moduli spaces, braid groups, monodromy, in addition to classical topology and algebraic geometry, combine to make this one of the most vibrant and active areas of research in mathematics. It is our hope that the five lectures of the present volume given at the C.I.M.E. Summer School held in Cetraro, Italy, September 2-10, 2003 will be useful to people working in related areas of mathematics and will become standard references on these topics. The volume is a coherent exposition of an active field of current research focusing on the introduction of new methods for the study of moduli spaces of complex structures on algebraic surfaces, and for the investigation of symplectic topology in dimension 4 and higher.

Spde In Hydrodynamics Recent Progress And Prospects

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Author : Sergio Albeverio
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-04-14

Spde In Hydrodynamics Recent Progress And Prospects written by Sergio Albeverio 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 2008-04-14 with Mathematics categories.

Of the three lecture courses making up the CIME summer school on Fluid Dynamics at Cetraro in 2005 reflected in this volume, the first, due to Sergio Albeverio describes deterministic and stochastic models of hydrodynamics. In the second course, Franco Flandoli starts from 3D Navier-Stokes equations and ends with turbulence. Finally, Yakov Sinai, in the 3rd course, describes some rigorous mathematical results for multidimensional Navier-Stokes systems and some recent results on the one-dimensional Burgers equation with random forcing.