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Harmonic Analysis On Finite Groups
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Author :Tullio Ceccherini-Silberstein Publisher :Cambridge University Press ISBN 13 :9780521883368 Total Pages :454 pages Book Rating :4.8/5 (833 download)
Book Synopsis Harmonic Analysis on Finite Groups by : Tullio Ceccherini-Silberstein
Download or read book Harmonic Analysis on Finite Groups written by Tullio Ceccherini-Silberstein and published by Cambridge University Press. This book was released on 2008-03-06 with total page 454 pages. Available in PDF, EPUB and Kindle. Book excerpt: Starting from a few concrete problems such as random walks on the discrete circle and the finite ultrametric space, this book develops the necessary tools for the asymptotic analysis of these processes. Its topics range from the basic theory needed for students new to this area, to advanced topics such as the theory of Green's algebras, the complete analysis of the random matchings, and a presentation of the presentation theory of the symmetric group. This self-contained, detailed study culminates with case-by-case analyses of the cut-off phenomenon discovered by Persi Diaconis.
Book Synopsis Fourier Analysis on Finite Groups and Applications by : Audrey Terras
Download or read book Fourier Analysis on Finite Groups and Applications written by Audrey Terras and published by Cambridge University Press. This book was released on 1999-03-28 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt: It examines the theory of finite groups in a manner that is both accessible to the beginner and suitable for graduate research.
Book Synopsis Fourier Analysis on Finite Abelian Groups by : Bao Luong
Download or read book Fourier Analysis on Finite Abelian Groups written by Bao Luong and published by Springer Science & Business Media. This book was released on 2009-08-14 with total page 167 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 :Tullio Ceccherini-Silberstein Publisher :Cambridge University Press ISBN 13 :1107182336 Total Pages :589 pages Book Rating :4.1/5 (71 download)
Book Synopsis Discrete Harmonic Analysis by : Tullio Ceccherini-Silberstein
Download or read book Discrete Harmonic Analysis written by Tullio Ceccherini-Silberstein and published by Cambridge University Press. This book was released on 2018-06-21 with total page 589 pages. Available in PDF, EPUB and Kindle. Book excerpt: A self-contained introduction to discrete harmonic analysis with an emphasis on the Discrete and Fast Fourier Transforms.
Book Synopsis Harmonic Analysis on Semigroups by : C. van den Berg
Download or read book Harmonic Analysis on Semigroups written by C. van den Berg and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 299 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Harmonic Analysis of Spherical Functions on Real Reductive Groups by : Ramesh Gangolli
Download or read book Harmonic Analysis of Spherical Functions on Real Reductive Groups written by Ramesh Gangolli and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 379 pages. Available in PDF, EPUB and Kindle. Book excerpt: Analysis on Symmetric spaces, or more generally, on homogeneous spaces of semisimple Lie groups, is a subject that has undergone a vigorous development in recent years, and has become a central part of contemporary mathematics. This is only to be expected, since homogeneous spaces and group representations arise naturally in diverse contexts ranging from Number theory and Geometry to Particle Physics and Polymer Chemistry. Its explosive growth sometimes makes it difficult to realize that it is actually relatively young as mathematical theories go. The early ideas in the subject (as is the case with many others) go back to Elie Cart an and Hermann Weyl who studied the compact symmetric spaces in the 1930's. However its full development did not begin until the 1950's when Gel'fand and Harish Chandra dared to dream of a theory of representations that included all semisimple Lie groups. Harish-Chandra's theory of spherical functions was essentially complete in the late 1950's, and was to prove to be the forerunner of his monumental work on harmonic analysis on reductive groups that has inspired a whole generation of mathematicians. It is the harmonic analysis of spherical functions on symmetric spaces, that is at the focus of this book. The fundamental questions of harmonic analysis on symmetric spaces involve an interplay of the geometric, analytical, and algebraic aspects of these spaces. They have therefore attracted a great deal of attention, and there have been many excellent expositions of the themes that are characteristic of this subject.
Book Synopsis Harmonic analysis on finite groups by : David A. Basin
Download or read book Harmonic analysis on finite groups written by David A. Basin and published by . This book was released on 1984 with total page 64 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Harmonic Analysis on Finite Groups by : Ceccherini-Silberstein Tullio Scarabotti Fabio Tolli Filippo
Download or read book Harmonic Analysis on Finite Groups written by Ceccherini-Silberstein Tullio Scarabotti Fabio Tolli Filippo and published by . This book was released on 2014-05-14 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt: Line up a deck of 52 cards on a table. Randomly choose two cards and switch them. How many switches are needed in order to mix up the deck? Starting from a few concrete problems such as random walks on the discrete circle and the finite ultrametric space this book develops the necessary tools for the asymptotic analysis of these processes. This detailed study culminates with the case-by-case analysis of the cut-off phenomenon discovered by Persi Diaconis. This self-contained text is ideal for graduate students and researchers working in the areas of representation theory, group theory, harmonic analysis and Markov chains. Its topics range from the basic theory needed for students new to this area, to advanced topics such as the theory of Green's algebras, the complete analysis of the random matchings, and the representation theory of the symmetric group.
Book Synopsis Fourier Analysis on Finite Groups with Applications in Signal Processing and System Design by : Radomir S. Stankovic
Download or read book Fourier Analysis on Finite Groups with Applications in Signal Processing and System Design written by Radomir S. Stankovic and published by John Wiley & Sons. This book was released on 2005-08-08 with total page 230 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis A First Course in Harmonic Analysis by : Anton Deitmar
Download or read book A First Course in Harmonic Analysis written by Anton Deitmar and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 154 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 :Tullio Ceccherini-Silberstein Publisher :Cambridge University Press ISBN 13 :1107627850 Total Pages :177 pages Book Rating :4.1/5 (76 download)
Book Synopsis Representation Theory and Harmonic Analysis of Wreath Products of Finite Groups by : Tullio Ceccherini-Silberstein
Download or read book Representation Theory and Harmonic Analysis of Wreath Products of Finite Groups written by Tullio Ceccherini-Silberstein and published by Cambridge University Press. This book was released on 2014-01-16 with total page 177 pages. Available in PDF, EPUB and Kindle. Book excerpt: A self-contained introduction to the representation theory and harmonic analysis of wreath products of finite groups, with examples and exercises.
Author :Tullio Ceccherini-Silberstein Publisher :Cambridge University Press ISBN 13 :1107729912 Total Pages :177 pages Book Rating :4.1/5 (77 download)
Book Synopsis Representation Theory and Harmonic Analysis of Wreath Products of Finite Groups by : Tullio Ceccherini-Silberstein
Download or read book Representation Theory and Harmonic Analysis of Wreath Products of Finite Groups written by Tullio Ceccherini-Silberstein and published by Cambridge University Press. This book was released on 2014-01-16 with total page 177 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents an introduction to the representation theory of wreath products of finite groups and harmonic analysis on the corresponding homogeneous spaces. The reader will find a detailed description of the theory of induced representations and Clifford theory, focusing on a general formulation of the little group method. This provides essential tools for the determination of all irreducible representations of wreath products of finite groups. The exposition also includes a detailed harmonic analysis of the finite lamplighter groups, the hyperoctahedral groups, and the wreath product of two symmetric groups. This relies on the generalised Johnson scheme, a new construction of finite Gelfand pairs. The exposition is completely self-contained and accessible to anyone with a basic knowledge of representation theory. Plenty of worked examples and several exercises are provided, making this volume an ideal textbook for graduate students. It also represents a useful reference for more experienced researchers.
Book Synopsis Harmonic Analysis on Classical Groups by : Gong Sheng
Download or read book Harmonic Analysis on Classical Groups written by Gong Sheng and published by Springer. This book was released on 1991 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: I. Harmonic Analysis on Unitary Groups.- 0. Preliminary.- 1. Abel Summation of Fourier Series on Unitary Groups.- 2. Cesàro Summations of Fourier Series on Unitary Groups.- 3. Partial Sum of Fourier Series on Unitary Groups.- 4. On Peter-Weyl Theorem.- 5. Spherical Summation of Fourier Series on Unitary Groups.- II. Harmonic Analysis on Rotation Groups.- 6. Abel Summation of Fourier Series on Rotation Groups.- 7. Cesàro Summation of Fourier Series on Rotation Groups.- 8. Partial Sum of Fourier Series on Rotation Groups.- 9. Spherical Summation of Fourier Series on Rotation Groups.- III. Harmonic Analysis on Unitary Symplectic Groups.- 10. The Volume of Unitary Symplectic Group and Criteria of Convergence of Fourier Series.- 11. Cesàro and Abel Summation of Fourier Series on Unitary Symplectic Groups.- 12. Spherical Summation of Fourier Series on Unitary Symplectic Groups.- 13. Harmonic Analysis in Classical Domains on Quaternion Field.- Epilogue.- References.
Book Synopsis A Course in Abstract Harmonic Analysis by : Gerald B. Folland
Download or read book A Course in Abstract Harmonic Analysis written by Gerald B. Folland and published by CRC Press. This book was released on 2016-02-03 with total page 317 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Book Synopsis Geometric Aspects of Harmonic Analysis by : Paolo Ciatti
Download or read book Geometric Aspects of Harmonic Analysis written by Paolo Ciatti and published by Springer Nature. This book was released on 2021-09-27 with total page 488 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume originated in talks given in Cortona at the conference "Geometric aspects of harmonic analysis" held in honor of the 70th birthday of Fulvio Ricci. It presents timely syntheses of several major fields of mathematics as well as original research articles contributed by some of the finest mathematicians working in these areas. The subjects dealt with are topics of current interest in closely interrelated areas of Fourier analysis, singular integral operators, oscillatory integral operators, partial differential equations, multilinear harmonic analysis, and several complex variables. The work is addressed to researchers in the field.
Book Synopsis Fourier Analysis on Number Fields by : Dinakar Ramakrishnan
Download or read book Fourier Analysis on Number Fields written by Dinakar Ramakrishnan and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Gelfand Triples and Their Hecke Algebras by : Tullio Ceccherini-Silberstein
Download or read book Gelfand Triples and Their Hecke Algebras written by Tullio Ceccherini-Silberstein and published by Springer Nature. This book was released on 2020-09-25 with total page 153 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph is the first comprehensive treatment of multiplicity-free induced representations of finite groups as a generalization of finite Gelfand pairs. Up to now, researchers have been somehow reluctant to face such a problem in a general situation, and only partial results were obtained in the one-dimensional case. Here, for the first time, new interesting and important results are proved. In particular, after developing a general theory (including the study of the associated Hecke algebras and the harmonic analysis of the corresponding spherical functions), two completely new highly nontrivial and significant examples (in the setting of linear groups over finite fields) are examined in full detail. The readership ranges from graduate students to experienced researchers in Representation Theory and Harmonic Analysis.
