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《三角级数》(Trigonometric Series)((美)Antoni Zygmund)扫描版[DJVU]

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  • 摘要:
    出版社Cambridge University Press
    发行时间1959年
    语言英文
  • 时间: 2010/06/05 20:37:19 发布 | 2010/06/05 21:24:56 更新
  • 分类: 图书  教育科技 

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中文名三角级数
原名Trigonometric Series
资源格式DJVU
版本扫描版
出版社Cambridge University Press
书号0521890535
发行时间1959年
地区美国
语言英文
简介

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内容简介:

Zygmund教授的这部著作1935年于波兰华沙首次出版时,便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。而第3版是将第2版的两卷合在一起,芝加哥大学数学系主任Robert Fefferman还特意为其作序,介绍作者的生平轶事、对数学分析的贡献以及本书的学术价值。

尽管本书的重点是使读者对主要概念有个全面的理解,但它同时还向读者介绍了实际数据分析的方方面面。本书适合作为高等院校数学及相关专业高年级本科生或研究生概率统计课程的教材,同时也可作为相关领域科技人员的参考资料。

内容截图:

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目录

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. Bessel's inequality and Parseval'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 sir]
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 Dirichlet-Jordan test
9. Gibbs's phenomenon p
10. The Dini-Lipschitz test
11. Lebesgue's test
12. Lebesgue constants
13. Poisson's summation formula
Miscellaneous theorems and examples
CHAPTER III
SUMMABILITY OF FOURIER SERIES
1. Summability of numerical series
2. General remarks about the summability of S[f] and S[f]
3. Summability of S[f] and S[f] by the method of the first arithmetic
mean
4. Convergence factors
5. Summability (C, a)
6. Abel summability
7. Abel summability (cont.)
8. Summability of S[dF] and S[dF]
9. Fourier series at simple discontinuities
10. Fourier sine series
11. Gibbs's phenomenon for the method (C, a)
12. Theorems of Rogosinski
13. Approximation to functions by trigonometric polynomials
Miscellaneous theorems and examples
CHAPTER IV
CLASSES OF FUNCTIONS AND FOURIER SERIES
1. The class L2
2. A theorem of Marcinkiewicz
3. Existence of the conjugate function
4. Classes of functions and (C, 1) means of Fourier series
5. Classes of functions and (C, 1) means of Fourier series (cont.)
6. Classes of functions and Abel means of Fourier series
7. Majorants for the Abel and Cesaro means of S[f]
8. Parseval's formula
9. Linear operations
10. Classes L
11. Conversion factors for classes of Fourier series
Miscellaneous theorems and examples
CHAPTER V
SPECIAL TRIGONOMETRIC SERIES
1. Series with coefficients tending monotonically to zero
2. The order of magnitude of functions represented by series with
monotone coefficients
3. A class of Fourier-Stieltjes series
4. The series
5. The series
6. Lacunary series
7. Riesz products
8. Rademacher series and their applications
9. Series with ' small' gaps
10. A power series of Salem
Miscellaneous theorems and examples
CHAPTER VI
THE ABSOLUTE CONVERGENCE OF TRIGONOMETRIC SERIES
1. General series
2. Sets N
3. The absolute convergence of Fourier series
4. Inequalities for polynomials
5. Theorems of Wiener and Levy
6. The absolute convergence of lacunary series
Miscellaneous theorems and examples
CHAPTER VII
COMPLEX METHODS IN FOURIER SERIES
1. Existence of conjugate functions
2. The Fourier character of conjugate series
3. Applications of Green's formula
4. Integrability B
5. Lipschitz conditions
6. Mean convergence of S[f] and S[f]
7. Classes Hp and N
8. Power series of bounded variation
9. Cauchy's integral
10. Conformal mapping
Miscellaneous theorems and examples
CHAPTER VIII
DIVERGENCE OF FOURIER SERIES
1. Divergence of Fourier series of continuous functions
2. Further examples of divergent Fourier series
3. Examples of Fourier series divergent almost everywhere
4. An everywhere divergent Fourier series
Miscellaneous theorems and examples
CHAPTER IX
RIEMANN'S THEORY OF TRIGONOMETRIC SERIES
1. General remarks. The Cantor-Lebesgue theorem
2. Formal integration of series
3. Uniqueness of the representation by trigonometric series
4. The principle of localization. Formal multiplication of trigonometric
series
5. Formal multiplication of trigonometric series (cont.)
6. Sets of uniqueness and sets of multiplicity
7. Uniqueness of summable trigonometric series
8. Uniqueness of summable trigonometric series (cont.)
9. Localization for series with coefficients not tending to zero
Miscellaneous theorems and examples
Notes

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