Aspects of Harmonic Analysis on Locally Compact Abelian Groups (局部緊緻阿貝爾群的調和分析面向)
Gallier, Jean H., Quaintance, Jocelyn
- 出版商: World Scientific Pub
- 出版日期: 2024-07-18
- 售價: $7,340
- 貴賓價: 9.5 折 $6,973
- 語言: 英文
- 頁數: 760
- 裝訂: Hardcover - also called cloth, retail trade, or trade
- ISBN: 9811291713
- ISBN-13: 9789811291715
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商品描述
The Fourier transform is a 'tool' used in engineering and computer vision to model periodic phenomena. Starting with the basics of measure theory and integration, this book delves into the harmonic analysis of locally compact abelian groups. It provides an in-depth tour of the beautiful theory of the Fourier transform based on the results of Gelfand, Pontrjagin, and Andre Weil in a manner accessible to an undergraduate student who has taken linear algebra and introductory real analysis.Highlights of this book include the Bochner integral, the Haar measure, Radon functionals, the theory of Fourier analysis on the circle, and the theory of the discrete Fourier transform. After studying this book, the reader will have the preparation necessary for understanding the Peter-Weyl theorems for complete, separable Hilbert algebras, a key theoretical concept used in the construction of Gelfand pairs and equivariant convolutional neural networks.
商品描述(中文翻譯)
傅里葉變換是一種在工程和計算機視覺中用來建模週期現象的「工具」。本書從測度理論和積分的基本概念開始,深入探討局部緊緻阿貝爾群的調和分析。它提供了一個深入的傅里葉變換理論之旅,基於Gelfand、Pontrjagin和Andre Weil的研究成果,以適合已修習線性代數和初級實分析的本科生的方式呈現。本書的亮點包括Bochner積分、Haar測度、Radon泛函、圓上的傅里葉分析理論以及離散傅里葉變換的理論。學習完本書後,讀者將具備理解完整可分Hilbert代數的Peter-Weyl定理所需的準備,這是一個在構建Gelfand對和等變卷積神經網絡中使用的關鍵理論概念。