Classical Fourier Analysis
暫譯: 古典傅立葉分析
Grafakos, Loukas
- 出版商: Springer
- 出版日期: 2014-11-19
- 售價: $3,110
- 貴賓價: 9.5 折 $2,955
- 語言: 英文
- 頁數: 638
- 裝訂: Hardcover - also called cloth, retail trade, or trade
- ISBN: 1493911937
- ISBN-13: 9781493911936
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相關主題
商品描述
The primary goal of this book is to present the theoretical foundation of the field of Euclidean Harmonic analysis. This book contains the classical topics such as interpolation, Fourier series, the Fourier transform, maximal functions, singular integrals, and Littlewood-Paley theory. This book is mainly addressed to graduate students in mathematics. The prerequisites are satisfactory completion of courses in real and complex variables. This book is intended to present the selected topics in depth and stimulate further study.
This third edition includes a new chapter entitled "Topics on Fourier series," which includes sections on Gibbs phenomenon, summability methods and Jackson's theorem, Tauberian theorems, spherical Fourier inversion, and Fourier transforms on the line. The new chapter ties really well with the material in the existing chapter 3 "Fourier Analysis on the Torus" and will prepare the students for (the existing) chapter 4.
In addition to a new chapter, the third edition contains 1000 different corrections and improvements in the existing text, more examples and applications, new and more relevant hints for the existing exercises, about 20-30 new exercises in the existing chapters, and improved references.
商品描述(中文翻譯)
這本書的主要目標是介紹歐幾里得調和分析領域的理論基礎。本書包含了經典主題，如插值、傅立葉級數、傅立葉變換、最大函數、奇異積分以及 Littlewood-Paley 理論。本書主要針對數學研究生，先修課程要求為實變數和複變數課程的滿意完成。本書旨在深入介紹選定主題並激發進一步的研究。
第三版新增了一章名為「傅立葉級數的主題」，該章節包括吉布斯現象、可和性方法及傑克遜定理、塔伯定理、球面傅立葉反演以及直線上的傅立葉變換。這一新章節與現有的第三章「圓環上的傅立葉分析」內容非常契合，並將為學生準備（現有的）第四章做準備。
除了新增一章外，第三版還對現有文本進行了1000處不同的修正和改進，增加了更多的例子和應用，為現有練習題提供了新的、更相關的提示，並在現有章節中增加了約20-30道新練習題，還改進了參考文獻。
作者簡介
Loukas Grafakos is a Professor of Mathematics at the University of Missouri at Columbia.
作者簡介(中文翻譯)
盧卡斯·格拉法科斯（Loukas Grafakos）是密蘇里大學哥倫比亞校區的數學教授。
