A first course in harmonic analysis
著者
書誌事項
A first course in harmonic analysis
（Universitext）
Springer, c2002
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注記
Includes bibliographical references (p. 147-149) and index
内容説明・目次
内容説明
This book is a primer in harmonic analysis on the undergraduate level. It gives a lean and streamlined introduction to the central concepts of this beautiful and utile theory. In contrast to other books on the topic, A First Course in Harmonic Analysis is entirely based on the Riemann integral and metric spaces instead of the more demanding Lebesgue integral and abstract topology. Nevertheless, almost all proofs are given in full and all central concepts are presented clearly.The first aim of this book is to provide an introduction to Fourier analysis, leading up to the Poisson Summation Formula. The second 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.
目次
Fourier Series * Hilbert Spaces * The Fourier Transform * Finite Abelian Groups * LCA-groups * The Dual Group * The Plancheral Theorem * Matrix Groups * The Representations of SU(2) * The Peter-Weyl Theorem * The Riemann zeta function * Haar integration.
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