Fourier Analysis On Groups

Author : Walter Rudin
Publisher : Courier Dover Publications
Page : 304 pages
File Size : 41,7 Mb
Release : 2017-04-19
Category : Mathematics
ISBN : 9780486821016

Get Book

Fourier Analysis on Groups by Walter Rudin Pdf

Written by a master mathematical expositor, this classic text reflects the results of the intense period of research and development in the area of Fourier analysis in the decade preceding its first publication in 1962. The enduringly relevant treatment is geared toward advanced undergraduate and graduate students and has served as a fundamental resource for more than five decades. The self-contained text opens with an overview of the basic theorems of Fourier analysis and the structure of locally compact Abelian groups. Subsequent chapters explore idempotent measures, homomorphisms of group algebras, measures and Fourier transforms on thin sets, functions of Fourier transforms, closed ideals in L1(G), Fourier analysis on ordered groups, and closed subalgebras of L1(G). Helpful Appendixes contain background information on topology and topological groups, Banach spaces and algebras, and measure theory.

Author : Bao Luong
Publisher : Springer Science & Business Media
Page : 167 pages
File Size : 53,6 Mb
Release : 2009-08-14
Category : Mathematics
ISBN : 9780817649166

Get Book

Fourier Analysis on Finite Abelian Groups by Bao Luong Pdf

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.

Author : Audrey Terras
Publisher : Cambridge University Press
Page : 456 pages
File Size : 46,6 Mb
Release : 1999-03-28
Category : Mathematics
ISBN : 0521457181

Get Book

Fourier Analysis on Finite Groups and Applications by Audrey Terras Pdf

It examines the theory of finite groups in a manner that is both accessible to the beginner and suitable for graduate research.

Author : Radomir S. Stankovic,Claudio Moraga,Jaakko Astola
Publisher : John Wiley & Sons
Page : 230 pages
File Size : 41,9 Mb
Release : 2005-08-08
Category : Science
ISBN : 9780471745426

Get Book

Fourier Analysis on Finite Groups with Applications in Signal Processing and System Design by Radomir S. Stankovic,Claudio Moraga,Jaakko Astola Pdf

Discover applications of Fourier analysis on finite non-Abeliangroups The majority of publications in spectral techniques considerFourier transform on Abelian groups. However, non-Abelian groupsprovide notable advantages in efficient implementations of spectralmethods. Fourier Analysis on Finite Groups with Applications in SignalProcessing and System Design examines aspects of Fourieranalysis on finite non-Abelian groups and discusses differentmethods used to determine compact representations for discretefunctions providing for their efficient realizations and relatedapplications. Switching functions are included as an example ofdiscrete functions in engineering practice. Additionally,consideration is given to the polynomial expressions and decisiondiagrams defined in terms of Fourier transform on finitenon-Abelian groups. A solid foundation of this complex topic is provided bybeginning with a review of signals and their mathematical modelsand Fourier analysis. Next, the book examines recent achievementsand discoveries in: Matrix interpretation of the fast Fourier transform Optimization of decision diagrams Functional expressions on quaternion groups Gibbs derivatives on finite groups Linear systems on finite non-Abelian groups Hilbert transform on finite groups Among the highlights is an in-depth coverage of applications ofabstract harmonic analysis on finite non-Abelian groups in compactrepresentations of discrete functions and related tasks in signalprocessing and system design, including logic design. All chaptersare self-contained, each with a list of references to facilitatethe development of specialized courses or self-study. With nearly 100 illustrative figures and fifty tables, this isan excellent textbook for graduate-level students and researchersin signal processing, logic design, and system theory-as well asthe more general topics of computer science and appliedmathematics.

Author : Dinakar Ramakrishnan,Robert J. Valenza
Publisher : Springer Science & Business Media
Page : 372 pages
File Size : 42,6 Mb
Release : 2013-04-17
Category : Mathematics
ISBN : 9781475730852

Get Book

Fourier Analysis on Number Fields by Dinakar Ramakrishnan,Robert J. Valenza Pdf

A modern approach to number theory through a blending of complementary algebraic and analytic perspectives, emphasising harmonic analysis on topological groups. The main goal is to cover John Tates visionary thesis, giving virtually all of the necessary analytic details and topological preliminaries -- technical prerequisites that are often foreign to the typical, more algebraically inclined number theorist. While most of the existing treatments of Tates thesis are somewhat terse and less than complete, the intent here is to be more leisurely, more comprehensive, and more comprehensible. While the choice of objects and methods is naturally guided by specific mathematical goals, the approach is by no means narrow. In fact, the subject matter at hand is germane not only to budding number theorists, but also to students of harmonic analysis or the representation theory of Lie groups. The text addresses students who have taken a year of graduate-level course in algebra, analysis, and topology. Moreover, the work will act as a good reference for working mathematicians interested in any of these fields.

Author : Cho-Ho Chu,Anthony To-Ming Lau
Publisher : Springer
Page : 100 pages
File Size : 51,6 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 : Elias M. Stein,Rami Shakarchi
Publisher : Princeton University Press
Page : 326 pages
File Size : 53,9 Mb
Release : 2011-02-11
Category : Mathematics
ISBN : 9781400831234

Get Book

Fourier Analysis by Elias M. Stein,Rami Shakarchi Pdf

This first volume, a three-part introduction to the subject, is intended for students with a beginning knowledge of mathematical analysis who are motivated to discover the ideas that shape Fourier analysis. It begins with the simple conviction that Fourier arrived at in the early nineteenth century when studying problems in the physical sciences--that an arbitrary function can be written as an infinite sum of the most basic trigonometric functions. The first part implements this idea in terms of notions of convergence and summability of Fourier series, while highlighting applications such as the isoperimetric inequality and equidistribution. The second part deals with the Fourier transform and its applications to classical partial differential equations and the Radon transform; a clear introduction to the subject serves to avoid technical difficulties. The book closes with Fourier theory for finite abelian groups, which is applied to prime numbers in arithmetic progression. In organizing their exposition, the authors have carefully balanced an emphasis on key conceptual insights against the need to provide the technical underpinnings of rigorous analysis. Students of mathematics, physics, engineering and other sciences will find the theory and applications covered in this volume to be of real interest. The Princeton Lectures in Analysis represents a sustained effort to introduce the core areas of mathematical analysis while also illustrating the organic unity between them. Numerous examples and applications throughout its four planned volumes, of which Fourier Analysis is the first, highlight the far-reaching consequences of certain ideas in analysis to other fields of mathematics and a variety of sciences. Stein and Shakarchi move from an introduction addressing Fourier series and integrals to in-depth considerations of complex analysis; measure and integration theory, and Hilbert spaces; and, finally, further topics such as functional analysis, distributions and elements of probability theory.

Author : Robert Hermann
Publisher : Addison Wesley Publishing Company
Page : 334 pages
File Size : 47,6 Mb
Release : 1969
Category : Fourier transformations
ISBN : UCAL:B3753971

Get Book

Fourier Analysis on Groups and Partial Wave Analysis by Robert Hermann Pdf

Author : Anton Deitmar
Publisher : Springer Science & Business Media
Page : 154 pages
File Size : 53,7 Mb
Release : 2013-04-17
Category : Mathematics
ISBN : 9781475738346

Get Book

A First Course in Harmonic Analysis by Anton Deitmar Pdf

This book introduces harmonic analysis at an undergraduate level. In doing so it covers Fourier analysis and paves the way for Poisson Summation Formula. Another central feature is that is makes the reader aware of the fact that both principal incarnations of Fourier theory, the Fourier series and the Fourier transform, are special cases of a more general theory arising in the context of locally compact abelian groups. The final goal of this book is to introduce the reader to the techniques used in harmonic analysis of noncommutative groups. These techniques are explained in the context of matrix groups as a principal example.

Author : Frédéric Barbaresco,Jean-Pierre Gazeau
Publisher : MDPI
Page : 260 pages
File Size : 49,5 Mb
Release : 2019-03-28
Category : Science
ISBN : 9783038977469

Get Book

Joseph Fourier 250th Birthday by Frédéric Barbaresco,Jean-Pierre Gazeau Pdf

For the 250th birthday of Joseph Fourier, born in 1768 in Auxerre, France, this MDPI Special Issue will explore modern topics related to Fourier Analysis and Heat Equation. Modern developments of Fourier analysis during the 20th century have explored generalizations of Fourier and Fourier–Plancherel formula for non-commutative harmonic analysis, applied to locally-compact, non-Abelian groups. In parallel, the theory of coherent states and wavelets has been generalized over Lie groups. One should add the developments, over the last 30 years, of the applications of harmonic analysis to the description of the fascinating world of aperiodic structures in condensed matter physics. The notions of model sets, introduced by Y. Meyer, and of almost periodic functions, have revealed themselves to be extremely fruitful in this domain of natural sciences. The name of Joseph Fourier is also inseparable from the study of the mathematics of heat. Modern research on heat equations explores the extension of the classical diffusion equation on Riemannian, sub-Riemannian manifolds, and Lie groups. In parallel, in geometric mechanics, Jean-Marie Souriau interpreted the temperature vector of Planck as a space-time vector, obtaining, in this way, a phenomenological model of continuous media, which presents some interesting properties. One last comment concerns the fundamental contributions of Fourier analysis to quantum physics: Quantum mechanics and quantum field theory. The content of this Special Issue will highlight papers exploring non-commutative Fourier harmonic analysis, spectral properties of aperiodic order, the hypoelliptic heat equation, and the relativistic heat equation in the context of Information Theory and Geometric Science of Information.

Author : Tullio Ceccherini-Silberstein,Fabio Scarabotti,Filippo Tolli
Publisher : Cambridge University Press
Page : 589 pages
File Size : 50,5 Mb
Release : 2018-06-21
Category : Mathematics
ISBN : 9781107182332

Get Book

Discrete Harmonic Analysis by Tullio Ceccherini-Silberstein,Fabio Scarabotti,Filippo Tolli Pdf

A self-contained introduction to discrete harmonic analysis with an emphasis on the Discrete and Fast Fourier Transforms.

Author : I. M. Gelfand,S. V. Fomin
Publisher : Courier Corporation
Page : 240 pages
File Size : 54,8 Mb
Release : 2012-04-26
Category : Mathematics
ISBN : 9780486135014

Get Book

Calculus of Variations by I. M. Gelfand,S. V. Fomin Pdf

Fresh, lively text serves as a modern introduction to the subject, with applications to the mechanics of systems with a finite number of degrees of freedom. Ideal for math and physics students.

Author : Gerald B. Folland
Publisher : CRC Press
Page : 317 pages
File Size : 42,5 Mb
Release : 2016-02-03
Category : Mathematics
ISBN : 9781498727150

Get Book

A Course in Abstract Harmonic Analysis by Gerald B. Folland Pdf

A Course in Abstract Harmonic Analysis is an introduction to that part of analysis on locally compact groups that can be done with minimal assumptions on the nature of the group. As a generalization of classical Fourier analysis, this abstract theory creates a foundation for a great deal of modern analysis, and it contains a number of elegant resul

Author : Sundaram Thangavelu
Publisher : Springer Science & Business Media
Page : 204 pages
File Size : 40,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461217725

Get Book

Harmonic Analysis on the Heisenberg Group by Sundaram Thangavelu Pdf

The Heisenberg group plays an important role in several branches of mathematics, such as representation theory, partial differential equations, number theory, several complex variables and quantum mechanics. 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 Euclidean harmonic analysis. The aim of this text is to demonstrate how the standard results of abelian harmonic analysis take shape in the non-abelian setup of the Heisenberg group. Thangavelu’s exposition is clear and well developed, and leads to several problems worthy of further consideration. Any reader who is interested in pursuing research on the Heisenberg group will find this unique and self-contained text invaluable.

Author : Eberhard Kaniuth,Anthony To-Ming Lau
Publisher : American Mathematical Soc.
Page : 306 pages
File Size : 50,5 Mb
Release : 2018-07-05
Category : Fourier analysis
ISBN : 9780821853658

Get Book

Fourier and Fourier-Stieltjes Algebras on Locally Compact Groups by Eberhard Kaniuth,Anthony To-Ming Lau Pdf

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.