Synopses & Reviews
This book is a primer in harmonic analysis using an elementary approach. Its first aim is to provide an introduction to Fourier analysis, leading up to the Poisson Summation Formula. Secondly, it makes the reader aware of the fact that both, 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 third goal of this book is to introduce the reader to the techniques used in harmonic analysis of noncommutative groups. There are two new chapters in this new edition. One on distributions will complete the set of real variable methods introduced in the first part. The other on the Heisenberg Group provides an example of a group that is neither compact nor abelian, yet is simple enough to easily deduce the Plancherel Theorem.
About the Author
Professor Deitmar holds a Chair in Pure Mathematics at the University of Exeter, U.K. He is a former Heisenberg fellow and was awarded the main prize of the Japanese Association of Mathematical Sciences in 1998. In his leisure time he enjoys hiking in the mountains and practicing Aikido.
Table of Contents
Fourier Series.- Hilbert Spaces.- The Fourier Transform.- Distributions.- Finite Abelian Groups.- LCA groups.- The Dual Group.- Plancheral's Theorem.- Matrix Groups.- The Representations of SU(2).- The Peter-Weyl Theorem.- The Heisenberg Group.- The Riemann Zeta Function.- Haar Integration.- Bibliography.- Index.
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