Harmonic Analysis on Classical Groups PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Harmonic Analysis on Classical Groups PDF full book. Access full book title Harmonic Analysis on Classical Groups by Gong Sheng. Download full books in PDF and EPUB format.
Author: Gong Sheng
Publisher: Springer
ISBN: 9783540176527
Category : Group theory
Languages : en
Pages : 0
Get Book Here
Book Description
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.
Author: Gong Sheng
Publisher: Springer
ISBN: 9783540176527
Category : Group theory
Languages : en
Pages : 0
Get Book Here
Book Description
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.
Author: Hans Reiter
Publisher: Oxford University Press on Demand
ISBN: 9780198511892
Category : Mathematics
Languages : en
Pages : 327
Get Book Here
Book Description
A revised and expanded second edition of Reiter's classic text Classical Harmonic Analysis and Locally Compact Groups (Clarendon Press 1968). It deals with various developments in analysis centring around around the fundamental work of Wiener, Carleman, and especially A. Weil. It starts with the classical theory of Fourier transforms in euclidean space, continues with a study at certain general function algebras, and then discusses functions defined on locally compact groups. The aim is, firstly, to bring out clearly the relations between classical analysis and group theory, and secondly, to study basic properties of functions on abelian and non-abelian groups. The book gives a systematic introduction to these topics and endeavours to provide tools for further research. In the new edition relevant material is added that was not yet available at the time of the first edition.
Author: Sheng Gong
Publisher:
ISBN:
Category : Group theory
Languages : en
Pages : 288
Get Book Here
Book Description
Author: Sundaram Thangavelu
Publisher: Springer Science & Business Media
ISBN: 1461217725
Category : Mathematics
Languages : en
Pages : 204
Get Book Here
Book Description
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: Camil Muscalu
Publisher: Cambridge University Press
ISBN: 1107031826
Category : Mathematics
Languages : en
Pages : 341
Get Book Here
Book Description
This contemporary graduate-level text in harmonic analysis introduces the reader to a wide array of analytical results and techniques.
Author: V. S. Varadarajan
Publisher: Cambridge University Press
ISBN: 9780521663625
Category : Mathematics
Languages : en
Pages : 326
Get Book Here
Book Description
Now in paperback, this graduate-level textbook is an introduction to the representation theory of semi-simple Lie groups. As such, it will be suitable for research students in algebra and analysis, and for research mathematicians requiring a readable account of the topic. The author emphasizes the development of the central themes of the sunject in the context of special examples, without losing sight of its general flow and structure. The book concludes with appendices sketching some basic topics with a comprehensive guide to further reading.
Author: Gregory S. Chirikjian
Publisher: CRC Press
ISBN: 1420041762
Category : Computers
Languages : en
Pages : 698
Get Book Here
Book Description
The classical Fourier transform is one of the most widely used mathematical tools in engineering. However, few engineers know that extensions of harmonic analysis to functions on groups holds great potential for solving problems in robotics, image analysis, mechanics, and other areas. For those that may be aware of its potential value, there is sti
Author: Camil Muscalu
Publisher: Cambridge University Press
ISBN: 0521882451
Category : Mathematics
Languages : en
Pages : 389
Get Book Here
Book Description
This contemporary graduate-level text in harmonic analysis introduces the reader to a wide array of analytical results and techniques.
Author: Donggao Deng
Publisher: Springer Science & Business Media
ISBN: 354088744X
Category : Mathematics
Languages : en
Pages : 167
Get Book Here
Book Description
This book could have been entitled “Analysis and Geometry.” The authors are addressing the following issue: Is it possible to perform some harmonic analysis on a set? Harmonic analysis on groups has a long tradition. Here we are given a metric set X with a (positive) Borel measure ? and we would like to construct some algorithms which in the classical setting rely on the Fourier transformation. Needless to say, the Fourier transformation does not exist on an arbitrary metric set. This endeavor is not a revolution. It is a continuation of a line of research whichwasinitiated,acenturyago,withtwofundamentalpapersthatIwould like to discuss brie?y. The ?rst paper is the doctoral dissertation of Alfred Haar, which was submitted at to University of Gottingen ̈ in July 1907. At that time it was known that the Fourier series expansion of a continuous function may diverge at a given point. Haar wanted to know if this phenomenon happens for every 2 orthonormal basis of L [0,1]. He answered this question by constructing an orthonormal basis (today known as the Haar basis) with the property that the expansion (in this basis) of any continuous function uniformly converges to that function.
Author: Gerrit van Dijk
Publisher: Walter de Gruyter
ISBN: 3110220202
Category : Mathematics
Languages : en
Pages : 234
Get Book Here
Book Description
This book is intended as an introduction to harmonic analysis and generalized Gelfand pairs. Starting with the elementary theory of Fourier series and Fourier integrals, the author proceeds to abstract harmonic analysis on locally compact abelian groups and Gelfand pairs. Finally a more advanced theory of generalized Gelfand pairs is developed. This book is aimed at advanced undergraduates or beginning graduate students. The scope of the book is limited, with the aim of enabling students to reach a level suitable for starting PhD research. The main prerequisites for the book are elementary real, complex and functional analysis. In the later chapters, familiarity with some more advanced functional analysis is assumed, in particular with the spectral theory of (unbounded) self-adjoint operators on a Hilbert space. From the contents Fourier series Fourier integrals Locally compact groups Haar measures Harmonic analysis on locally compact abelian groups Theory and examples of Gelfand pairs Theory and examples of generalized Gelfand pairs
