Deitmar A. A First Course in Harmonic Analysis

2nd ed.— Springer, 2005. — 189 p. — ISBN: 0387228373.This book is intended as a primer in harmonic analysis at the upper undergraduate or early graduate level. All central concepts of har- monic analysis are introduced without too much technical overload. For example, the book is based entirely on the Riemann integral in- stead of the more demanding Lebesgue integral. Furthermore, all topological questions are dealt with purely in the context of metric spaces. It is quite surprising that this works. Indeed, it turns out that the central concepts of this beautiful and useful theory can be explained using very little technical background.The first aim of this book is to give a lean introduction to Fourier analysis, leading up to the Poisson summation formula. The sec- ond aim is to make 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 third 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. The first part of the book deals with Fourier analysis. Chapter