概率框架下恒等算子的线性n-宽度
Linear n-Width of Identity Operators in Probabilistic Setting
摘要:
本文讨论了恒等算子在概率框架Ip,q:lp,r→{1≤q≤q<∞,r>1/q-1/p }下的线性(n, δ)-宽度,并计算了其精确渐近阶。
Abstract:
In this paper, we discuss the Linear (n, δ)-width of identity operator in probabilistic setting Ip,q:lp,r→{1≤q≤q<∞,r>1/q-1/p }, and obtained its accurate asymptotic degree.
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 Beste Annaherung Von Funktionen Einer Gegebenen Funktionenklasse. Annals of Mathematics, 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. (In Russian)
|
|
[4]
|
Tikhomirov, V.M. (1960) Diameters of Sets in Function Spaces and the Theory of Best Approximations. Russian Mathematical Surveys, 15, 75. [Google Scholar] [CrossRef]
|
|
[5]
|
Pietsch, A. (1974) S-Numbers of Operators in Banach Spaces. Studia Mathematica, 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, 220, 1278-1281.
|
|
[7]
|
Ismagilov, R.S. (1974) Diameters of Sets in Normed Linear Spaces and Approximation of Functions by Trigonometric Polynomials. Russian Mathematical Surveys, 29, 161-178. [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[D]. 成都: 西华大学, 2018.
|