三角级数 Trigonometric Series 美 Antoni Zygmund 扫描版[DJVU]

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资源信息： 中文名: 三角级数 原名: Trigonometric Series 作者: (美)Antoni Zygmund 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 概述:

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:

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