导语

  

内容提要

  

    这一套经典著作初版于1935年，之后在学术界确立了其典范地位。第1版虽然对细节问题没有展开详尽讨论，但对当时的主要研究成果都给予了简要说明。1959年，剑桥大学出版社分两卷出版了该书第2版，书中全面介绍了三角级数的基本概念，同时涉及实际数据分析等相关内容。书中加进了自第1版以来在三角级数、傅里叶级数以及纯数学各相关分支中的研究成果，对原书做了重大扩充。而吉格曼编著的《三角级数(第1卷第3版)(英文版)》是将第2版的两卷合在一起，芝加哥大学数

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