Fourier Analysis on Groups: Rudin/Fourier
Fourier Analysis on Groups: Rudin/Fourier
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DOI：
10.1002/9781118165621
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发表时间：
1990-01
期刊：
影响因子：
--
通讯作者：
W. Rudin
中科院分区：
文献类型：
--
作者：
W. Rudin
这本经典著作由一位数学大师撰写，反映了傅立叶分析领域在1962年首次出版之前的十年中紧张的研究和发展时期的结果。相关的治疗是面向高级本科生和研究生，并已作为一个基本资源超过五十年。自包含的文本打开傅立叶分析的基本定理和局部紧阿贝尔群的结构的概述。随后的章节探讨幂等测度，群代数的同态，薄集上的测度和傅立叶变换，傅立叶变换的函数，L1（G）中的闭理想，有序群上的傅立叶分析，以及L1（G）的闭子代数。有用的参考书目包含拓扑学和拓扑群、Banach空间和代数以及测度论的背景信息。
Written by a master mathematical expositor, this classic text reflects the results of the intense period of research and development in the area of Fourier analysis in the decade preceding its first publication in 1962. The enduringly relevant treatment is geared toward advanced undergraduate and graduate students and has served as a fundamental resource for more than five decades. The self-contained text opens with an overview of the basic theorems of Fourier analysis and the structure of locally compact Abelian groups. Subsequent chapters explore idempotent measures, homomorphisms of group algebras, measures and Fourier transforms on thin sets, functions of Fourier transforms, closed ideals in L1 (G), Fourier analysis on ordered groups, and closed subalgebras of L1 (G). Helpful Appendixes contain background information on topology and topological groups, Banach spaces and algebras, and measure theory.