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三角级数 第2卷 第3版PDF|Epub|txt|kindle电子书版本下载
- 吉格曼 著
- 出版社： 北京;西安：世界图书出版公司
- ISBN：7519209971
- 出版时间：2016
- 标注页数：364页
- 文件大小：55MB
- 文件页数：371页
- 主题词：
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图书目录
CHAPTER Ⅹ TRIGONOMETRIC INTERPOLATION1
1．General remarks1
2．Interpolating polynomials as Fourier series6
3．The case of an even number of fundamental points8
4．Fourier-Lagrange coefficients14
5．Convergence of interpolating polynomials16
6．Jackson polynomials and related topics21
7．Mean convergence of interpolating polynomials27
8．Divergence ofinterpolating polynomials35
9．Divergence of interpolating polynomials（cont.）44
10．Polynomials conjugate to interpolating polynomials48
Miscellaneous theorems and examples55
CHAPTER Ⅺ DIFFERENTIATION OF SERIES.GENERALIZED DERIVATIVES55
1．Cesàro summability of differentiated series59
2．Summability C of Fourier series65
3．A theorem on differentiated series71
4．Theorems on generalized derivatives73
5．Applications of Theorem（4·2）to Fourier series80
6．The integral M and Fourier series83
7．The integral M286
Miscellaneous theorems and examples91
CHAPTER Ⅻ INTERPOLATION OF LINEAR OPERATIONS.MORE ABOUT FOURIER COEFFICIENTS91
1．The Riesz-Thorin theorem93
2．The theorems of Hausdorff-Young and F.Riesz101
3．Interpolation of operations in the classes Hr105
4．Marcinkiewicz's theorem on the interpolation of operations111
5．Paley's theorems on Fourier coefficients120
6．Theorems of Hardy and Littlewood about rearrangements of Fourier coefficients127
7．Lacunary coefficients131
8．Fractional integration133
9．Fractional integration（cont.）138
10．Fourier-Stieltjes coefficients142
11．Fourier-Stieltjes coefficients and sets of constant ratio of dissection147
Miscellaneous theorems and examples156
CHAPTER ⅩⅢ CONVERGENCE AND SUMMABILITY ALMOST EVERYWHERE156
1．Partial sums of S［f］for f∈L2161
2．Order of magnitude of Sn for f∈Lp166
3．A test for the convergence of S［f］almost everywhere170
4．Majorants for the partial sums of S［f］and ？［f］173
5．Behaviour of the partial sums of S［f］and ？［f］175
6．Theorems on the partial sums of power sories178
7．Strong summability of Fourier series.The case f∈Lr,r＞1180
8．Strong summability of S［f］and ？［f］in the general case184
9．Almost convergence of S［f］and ？［f］188
10．Theorems on the convergence of orthogonal series189
11．Capacity of sets and convergence of Fourier series194
Miscellaneous theorems and examples197
CHAPTER ⅩⅣ MORE ABOUT COMPLEX METHODS199
1．Boundary behaviour of harmonic and analytic functions199
2．The function s（θ）207
3．The Littlewood-Paley function g（θ）210
4．Convergence of conjugate series216
5．The Marcinkiewicz functionμ（θ）219
Miscellaneous theorems and examples221
CHAPTER ⅩⅤ APPLICATIONS OF THE LITTLEWOOD-PALEY FUNCTION TO FOURIER SERIES221
1．General remarks222
2．Functions in Lr,l＜r＜∞224
3．Functions in Lr,l＜r＜∞（cont.）229
4．Theorems on the partial sums of S［f］,f∈Lr,l＜r＜∞230
5．The limiting case r=l234
6．The limiting case r=∞239
CHAPTER ⅩⅥ FOURIER INTEGRALS242
1．General remarks242
2．Fourier transforms246
3．Fourier transforms（cont.）254
4．Fourier-Stieltjes transforms258
5．Applications to trigonometric series263
6．Applications to trigonometric series（cont.）269
7．The Paley-Wiener theorem272
8．Riemann theory of trigonometric integrals278
9．Equiconvergence theorems286
10．Problems of uniqueness291
Miscellaneous theorems and examples297
CHAPTER ⅩⅦ A TOPIC IN MULTIPLE FOURIER SERIES300
1．General remarks300
2．Strong differentiability of multiple integrals and its applications305
3．Restricted summability of Fourier series309
4．Power series of several variables315
5．Power series of several variables（cont.）321
Miscellaneous theorems and examples328
Notes331
Bibtiography336
Index353