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A Course in Abstract Harmonic Analysis (2E) by Gerald B. Folland
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**About this book :- **
**A Course in Abstract Harmonic Analysis (2E) ** written by
** Gerald B. Folland **

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 results and techniques that are of interest in their own right.

This book develops the abstract theory along with a well-chosen selection of concrete examples that exemplify the results and show the breadth of their applicability. After a preliminary

containing the necessary background material on Banach algebras and spectral theory, the text sets out the general theory of locally compact groups and their unitary representations, followed by a development of the more specific theory of analysis on Abelian groups and compact groups. There is an extensive

on the theory of induced representations and its applications, and the book concludes with a more informal exposition on the theory of representations of non-Abelian, non-compact groups.

Featuring extensive updates and new examples, the Second Edition: Adds a short section on von Neumann algebras. Includes Mark Kac’s simple proof of a restricted form of Wiener’s theorem. Explains the relation between SU(2) and SO(3) in terms of quaternions, an elegant method that brings SO(4) into the picture with little effort. Discusses representations of the discrete Heisenberg group and its central quotients, illustrating the Mackey machine for regular semi-direct products and the pathological phenomena for nonregular ones.

A Course in Abstract Harmonic Analysis, Second Edition serves as an entrée to advanced mathematics, presenting the essentials of harmonic analysis on locally compact groups in a concise and accessible form.

(Gerald B. Folland)

**Book Detail :- **
** Title: ** A Course in Abstract Harmonic Analysis
** Edition: ** 2nd
** Author(s): ** Gerald B. Folland
** Publisher: ** Chapman and Hall/CRC
** Series: ** Textbooks in Mathematics
** Year: ** 2015
** Pages: ** 318
** Type: ** PDF
** Language: ** English
** ISBN: ** 1498727131,9781498727136,9781498727150
** Country: ** US

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**About Author :- **

Author ** Gerald Budge Folland ** is an American mathematician and a professor of mathematics at the University of Washington. His areas of interest are harmonic analysis (on both Euclidean space and Lie groups), differential equations, and mathematical physics. The title of his doctoral dissertation at Princeton University (1971) is "The Tangential Cauchy-Riemann Complex on Spheres".

He is the author of several textbooks in mathematical analysis. In 2012 he became a fellow of the American Mathematical Society.

**All Famous Books of this Author :- **

Here is list all books, text books, editions, versions or solution manuals avaliable of this author, We recomended you to download all.

** • Download PDF Real Analysis 2E: Modern Techniques and Their Applications by Gerald B. Folland **

** • Download PDF A Guide to Advanced Real Analysis by Gerald B. Folland **

** • Download PDF A Course in Abstract Harmonic Analysis (2E) by Gerald B. Folland **

** • Download PDF Partial Differential Equations (2E) by Gerald B. Folland **

** • Download PDF Advanced Calculus by Gerald B. Folland **

** • Download PDF Fourier Analysis and Its Applications by Gerald B. Folland **

** • Download PDF Quantum Field Theory by Gerald B. Folland **

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**Book Contents :- **
**A Course in Abstract Harmonic Analysis (2E) ** written by
** Gerald B. Folland **
cover the following topics.

1. Banach Algebras and Spectral Theory

2. Locally Compact Groups

3. Basic Representation Theory

4. Analysis on Locally Compact Abelian Groups

5. Analysis on Compact Groups

6. Induced Representations

7. Further Topics in Representation Theory

Appendices

Bibliography

Index

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