A Course in Abstract Harmonic Analysis
Title | A Course in Abstract Harmonic Analysis PDF eBook |
Author | Gerald B. Folland |
Publisher | CRC Press |
Pages | 317 |
Release | 2016-02-03 |
Genre | 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
Principles of Harmonic Analysis
Title | Principles of Harmonic Analysis PDF eBook |
Author | Anton Deitmar |
Publisher | Springer |
Pages | 330 |
Release | 2014-06-21 |
Genre | 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.
Introduction to Abstract Harmonic Analysis
Title | Introduction to Abstract Harmonic Analysis PDF eBook |
Author | Lynn H. Loomis |
Publisher | Courier Corporation |
Pages | 210 |
Release | 2013-05-09 |
Genre | 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.
A First Course in Harmonic Analysis
Title | A First Course in Harmonic Analysis PDF eBook |
Author | Anton Deitmar |
Publisher | Springer Science & Business Media |
Pages | 154 |
Release | 2013-04-17 |
Genre | 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.
An Introduction to Harmonic Analysis
Title | An Introduction to Harmonic Analysis PDF eBook |
Author | Yitzhak Katznelson |
Publisher | |
Pages | 292 |
Release | 1968 |
Genre | Harmonic analysis |
ISBN |
The Bellman Function Technique in Harmonic Analysis
Title | The Bellman Function Technique in Harmonic Analysis PDF eBook |
Author | Vasily Vasyunin |
Publisher | Cambridge University Press |
Pages | 465 |
Release | 2020-08-06 |
Genre | Mathematics |
ISBN | 1108486894 |
A comprehensive reference on the Bellman function method and its applications to various topics in probability and harmonic analysis.
Elements of Abstract Harmonic Analysis
Title | Elements of Abstract Harmonic Analysis PDF eBook |
Author | George Bachman |
Publisher | Elsevier |
Pages | 269 |
Release | 2013-10-22 |
Genre | Mathematics |
ISBN | 1483267563 |
Elements of Abstract Harmonic Analysis provides an introduction to the fundamental concepts and basic theorems of abstract harmonic analysis. In order to give a reasonably complete and self-contained introduction to the subject, most of the proofs have been presented in great detail thereby making the development understandable to a very wide audience. Exercises have been supplied at the end of each chapter. Some of these are meant to extend the theory slightly while others should serve to test the reader's understanding of the material presented. The first chapter and part of the second give a brief review of classical Fourier analysis and present concepts which will subsequently be generalized to a more abstract framework. The next five chapters present an introduction to commutative Banach algebras, general topological spaces, and topological groups. The remaining chapters contain some of the measure theoretic background, including the Haar integral, and an extension of the concepts of the first two chapters to Fourier analysis on locally compact topological abelian groups.