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內容簡介

　　這一套經典著作初版於1935年，之後在學術界確立瞭其典範地位。第一版雖然對細節問題沒有展開詳盡討論，但對當時的主要研究成果都給予瞭簡要說明。1959年，劍橋大學齣版社分兩捲齣版瞭該書第2版，書中全麵介紹瞭三角級數的基本概念，同時涉及實際數據分析等相關內容。書中加進瞭自第一版以來在三角級數、傅裏葉級數以及純數學各相關分支中的研究成果，對原書做瞭重大擴充。而《三角級數（第1捲 第3版 英文版）》是將第2版的兩捲閤在一起，芝加哥大學數

目錄

Preface
List of Symbols

CHAPTER Ⅰ
TRIGONOMETRIC SERIES AND FOURIER SERIES．
AUXILIARY RESULTS
1． Trigonometric series
2． Summation by parts
3． Orthogonal series
4． The trigonometric system
5． Fourier-Stieltjes series
6． Completeness of'the trigonometric system
7． Bossel's inequality and Parsoval's formula
8． Remarks on series and integrals
9． Inequalities
10． Convex functions
11． Convergence in Lr
12． Sets of the first and second categories
13． Rearrangements of functions． Maximal theorems of Hardy and
Littlewood
Miscellaneous theorems and examples

CHAPTER Ⅱ
FOURIER COEFFICIENTS． ELEMENTARY THEOREMS ON
THE CONVERGENCE OF s[f] AND s[f]
1． Formal operations on s[f]
2． Differentiation and integration of s[f]
3． Modulus of continuity． Smooth functions
4． Order of magnitude of Fourier coefficients
5． Formulae for partial sums of s[f] and s[f]
6． The Dini test and the principle of localization
7． Some more formulae for partial sums
8． The Diriehlet-Jordan test
……

CHAPTER Ⅲ SUMMABILITY OF FOURIES SERIES
CHAPTER Ⅳ CLASSES OF FUNCTIONS AND FOURIER SERIES
CHAPTER Ⅴ SPECIAL TRIGONOMERIC SERIES
CHAPTER Ⅵ THE SBSOLUTE CONVERGENCE OF TRIGONOMETRIC SERIES
CHAPTER Ⅶ COMPLEX METHODS IN FOURIER SERIES
CHAPTER Ⅷ DIVERGENCE OF FOURIER SERIES
CHAPTER Ⅸ RIEMANN'S THEORY OF TRIGONOMETRIC SERIES
三角級數（第1捲 第3版 英文版） [rigonometric Series Vol.1 Third Edition] 下載 mobi epub pdf txt 電子書

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