Principles of Harmonic Analysis 2024 pdf epub mobi 电子书

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发表于2024-12-23

Principles of Harmonic Analysis 2024 pdf epub mobi 电子书

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出版者:Springer

作者:Anton Deitmar

出品人:

页数:333

译者:

出版时间:2008-11-21

价格:USD 59.99

装帧:Paperback

isbn号码:9780387854687

丛书系列:

图书标签: 数学调和分析分析调和分析7 of Springer Principles Harmonic

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The book is written for graduate students who have read the first book and like to see the proofs which were not given there and/or want to see the full extent of the theory. On the other hand it can be read independently from the first one, only a modest knowledge on Fourier series/tranform is required to understand the examples. This book fills a major gap in the textbook literature, as a full proof of Pontryagin Duality and Plancherel Theorem is hard to come by. It is usually given in books that focus on C*-algebras and thus carry too much technical overload for the reader who only wants these basic results of Harmonic Analysis. Other proofs use the structure theory which carries the reader away in a different direction. Here the authors consider the Banach-algebra approach more elegant and enlighting. They provide a streamlined approach that reaches the main results directly, and they also give the generalizations to the non-Abelian case. Another main pillar of Harmonic analysis is the Poisson Summation Formula. We give its generalization to LCA-groups. The Selberg Trace Formula is considered the generalization of the Poisson Formula to non-abelian groups. The authors give the first textbook approach to this deep and useful formula in full generality. The last two chapters are devoted to examples of applications of the Selberg Trace Formula.

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群表示是单射或者就是嵌入； Selberg trace formula ：zeta函数的零点和素数的对偶；推广到紧黎曼曲面的测地线的长度对偶于拉普拉斯算子的谱，是经典调和分析中的泊松公式（函数的周期化的傅里叶系数和整数上的傅里叶变换等价提供了圆上的函数和直线上函数的关系）调和的非交换推广.Peter–Weyl 定理是紧群的傅里叶分析中Plancherel定理推广，也是有限群的正规表示的推论。群的矩阵系数是线性泛函与表示的合成；函数的傅里叶系数是线性泛函与正弦函数的合成。

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