三角级数(第2卷第3版)(英文版)

吉格曼著的《三角级数(第2卷第3版)(英文版)》 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。

CHAPTER X TRIGONOMETRIC INTERPOLATION 1. General remarks 2. Interpolating polynomials as Fourier series 3. The case of an oven number of fundamental points 4. Fourior-Lagrange coefficients 5. Convergence of interpolating polynomials 6. Jackson polynomials and related topics 7. Mean convergence of interpolating polynomials 8. Divergence of interpolating polynomials 9. Divergence of interpolating polynomials (cont.) 10. Polynomials conjugate to interpolating polynomials Miscellaneous theorems and examples CHAPTER XI DIFFERENTIATION OF SERIES. GENERALIZED DERIVATIVES 1. Cesaro summability of differentiated series 2. Summability C of Fourier series 3. A theorem on differentiated series 4. Theorems on generalized derivatives 5. Applications of Theorem (4-2) to Fourier series 6. The integral M and Fourier series 7. The integral Ms Miscellaneous theorems and examples CHAPTER XII INTERPOLATION OF LINEAR OPERATIONS. MORE ABOUT FOURIER COEFFICIENTS 1. The Riesz-Tborin theorem 2. The theorems of Hausdorff-Young and F. Riesz 3. Interpolation of operations in the classes Hr 4. Marcinkiewicz's theorem on the interpolation of operations 5. Paley's theorems on Fourier coefficients 6. Theorems of Hardy and Littlewood about rearrangements of Fourier coefficients 7. Lacunary coefficients 8. Fractional integration 9. Fractional integration (cont.) 10. Fourier-Stieltjes coefficients 11. Fourier-Stie]tjes coefficients and sets of constant ratio of dissection Miscellaneous theorems and examples CHAPTER XlII CONVERGENCE AND SUMMABILITY ALMOST EVERYWHERE 1. Partial sums of S[f] for f∈L2 2. Order of- magnitude of Sn for f∈Lp 3. A test for the convergence of S[f] almost everywhere 84. Majorants for the partial sums of Sill and S[f] 5. Behaviour of the partial sums of S[f] and S[f] 6. Theorems on the partial sums of power series 7. Strong summability of Fourier series. The case f∈ Lr, r > 1 8. Strong summability of S[f] and S[f] in the general case 9. Almost convergence of S[f] and S[f] 10. Theorems on the convergence of orthogonal series 11. Capacity of sets and convergence of Fourier series Miscellaneous theorems and examples CHAPTER XIV MORE ABOUT COMPLEX METHODS 1. Boundary behaviour of harmonic and analytic functions 2. The function S(θ) 3. The Littlewood-Paley function g(θ) 4. Convergence of conjugate series 5. The Marcinkiewicz function μ(θ) Miscellaneous theorems and examples CHAPTER XV APPLICATIONS OF THE LITTLEWOOD-PALEY FUNCTION TO FOURIER SERIES 1. General remarks 2. Functions in Lr, 1 < r <∞ 3. Functions in Lr, 1