概率框架下无穷维恒等算子的Kolmogorov (n,δ)-宽度
Kolmogorov -Width of Infinite-Dimension Identity Operators in Probabilistic Frames
摘要: 本文讨论了无穷维恒等算子在概率框架下的宽度,并计算了其精确渐近阶。
Abstract: In this paper, we consider the Kolmogorov (n,δ)-width of infinite-dimension identity operator in probabilistic frames, and obtain its asymptotic degree.
文章引用:陈锦, 肖寒月. 概率框架下无穷维恒等算子的Kolmogorov (n,δ)-宽度[J]. 应用数学进展, 2019, 8(5): 902-909. https://doi.org/10.12677/AAM.2019.85102

参考文献

[1] Traub, J.F., Wasilkowski, G.W. and Wozniakowski, H. (1988) Information-Based Complexity. Academic Press, Bos-ton.
[2] Kolmogorov, A.N. (1936) Uber die deste Annaherung yon funktionen einer gegebenen funktioneklasse. An-nals of Mathematics, No. 37, 107-111. [Google Scholar] [CrossRef
[3] Stechkin, S.R. (1954) On Best Ap-proximation of Given Classes of Functions by Arbitrary Polynomials. Uspekhi Matematicheskikh Nauk, 9, 133-134. (Russian)
[4] Tikhomirov, V.M. (1960) Diameters of Sets in Function Spaces and the Theory of Best Approximations. Uspekhi Matematicheskikh Nauk, 15, 81-120. (English Translation in Russian Mathematical Surveys, 15, 75-111.) [Google Scholar] [CrossRef
[5] Pietsch, A. (1974) S-Numbers of Operators in Ba-nach Spaces. Studia Mathematica, No. 51, 201-223. [Google Scholar] [CrossRef
[6] Stesin, M.I. (1975) Aleksandrov Widths of Finite-Dimensional Sets and Classes of Smooth Functions. Doklady Akademii Nauk SSSR, 220, 1278-1281. (English Translation in Soviet Mathematics, Doklady)
[7] Ismagilov, R.S. (1974) Widths of Sets in Normed Linear Spaces and Approximation of Functions by Trigonometric Polynomials. Uspekhi Matematicheskikh Nauk, 29, 161-178. (English Translation in Russian Mathematical Surveys, 29, 169-186.) [Google Scholar] [CrossRef
[8] Pinkus, A. (1985) N-Widths in Approximation Theory. Springer, Berlin. [Google Scholar] [CrossRef
[9] 王桐心. 无穷维恒等算子的Kolmogorov n-宽度[J]. 应用数学进展, 2018, 7(5): 519-524.
[10] Maiorov, V.E. (1994) Kolmogorov’s -Widths of the Spaces of the Smooth Functions. Russian Academy of Sciences. Sbornik Mathe-matics, 79, 265-279. [Google Scholar] [CrossRef