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Author : Yitzhak Katznelson
Publisher :
Page : 292 pages
File Size : 13,56 MB
Release : 1968
Category : Harmonic analysis
ISBN :
Author : Yitzhak Katznelson
Publisher : Cambridge University Press
Page : 342 pages
File Size : 32,4 MB
Release : 2004-01-05
Category : Mathematics
ISBN : 9780521543590
Publisher description
Author : Lynn H. Loomis
Publisher : Courier Corporation
Page : 210 pages
File Size : 42,14 MB
Release : 2013-05-09
Category : Mathematics
ISBN : 0486282317
Written by a prominent figure in the field of harmonic analysis, this classic monograph is geared toward advanced undergraduates and graduate students and focuses on methods related to Gelfand's theory of Banach algebra. 1953 edition.
Author : V. S. Varadarajan
Publisher : Cambridge University Press
Page : 326 pages
File Size : 35,8 MB
Release : 1999-07-22
Category : Mathematics
ISBN : 9780521663625
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 : Gerrit van Dijk
Publisher : Walter de Gruyter
Page : 234 pages
File Size : 46,30 MB
Release : 2009-12-23
Category : Mathematics
ISBN : 3110220202
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
Author : María Cristina Pereyra
Publisher : American Mathematical Soc.
Page : 437 pages
File Size : 40,72 MB
Release : 2012
Category : Mathematics
ISBN : 0821875663
Conveys the remarkable beauty and applicability of the ideas that have grown from Fourier theory. It presents for an advanced undergraduate and beginning graduate student audience the basics of harmonic analysis, from Fourier's study of the heat equation, and the decomposition of functions into sums of cosines and sines (frequency analysis), to dyadic harmonic analysis, and the decomposition of functions into a Haar basis (time localization).
Author : Anton Deitmar
Publisher : Springer Science & Business Media
Page : 154 pages
File Size : 42,31 MB
Release : 2013-04-17
Category : Mathematics
ISBN : 147573834X
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 : Anton Deitmar
Publisher : Springer
Page : 330 pages
File Size : 18,68 MB
Release : 2014-06-21
Category : Mathematics
ISBN : 3319057928
This book offers a complete and streamlined treatment of the central principles of abelian harmonic analysis: Pontryagin duality, the Plancherel theorem and the Poisson summation formula, as well as their respective generalizations to non-abelian groups, including the Selberg trace formula. The principles are then applied to spectral analysis of Heisenberg manifolds and Riemann surfaces. This new edition contains a new chapter on p-adic and adelic groups, as well as a complementary section on direct and projective limits. Many of the supporting proofs have been revised and refined. The book is an excellent resource for graduate students who wish to learn and understand harmonic analysis and for researchers seeking to apply it.
Author : Gerald B. Folland
Publisher : CRC Press
Page : 317 pages
File Size : 35,24 MB
Release : 2016-02-03
Category : Mathematics
ISBN : 1498727158
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 : Thomas H. Wolff
Publisher : American Mathematical Soc.
Page : 154 pages
File Size : 42,23 MB
Release : 2003-09-17
Category : Mathematics
ISBN : 0821834495
This book demonstrates how harmonic analysis can provide penetrating insights into deep aspects of modern analysis. It is both an introduction to the subject as a whole and an overview of those branches of harmonic analysis that are relevant to the Kakeya conjecture. The usual background material is covered in the first few chapters: the Fourier transform, convolution, the inversion theorem, the uncertainty principle and the method of stationary phase. However, the choice of topics is highly selective, with emphasis on those frequently used in research inspired by the problems discussed in the later chapters. These include questions related to the restriction conjecture and the Kakeya conjecture, distance sets, and Fourier transforms of singular measures. These problems are diverse, but often interconnected; they all combine sophisticated Fourier analysis with intriguing links to other areas of mathematics and they continue to stimulate first-rate work. The book focuses on laying out a solid foundation for further reading and research. Technicalities are kept to a minimum, and simpler but more basic methods are often favored over the most recent methods. The clear style of the exposition and the quick progression from fundamentals to advanced topics ensures that both graduate students and research mathematicians will benefit from the book.