无穷维序列空间的线性n-宽度
Linear n-Width of Infinite-Dimensional Sequence Space
摘要:
本文讨论了无穷维序列空间的线性n-宽度,并估计其精确渐近阶。
Abstract:
The linear n-width of infinite-dimensional sequence space is discussed in this paper, and its sharp asymptotic order is estimated.
参考文献
|
[1]
|
Kolmogorov, A.N. (1936) Uber die deste Annaherung von funktionen einer gegebenen funktioneklasse. Annals of Mathematics, No. 37, 107-111. [Google Scholar] [CrossRef]
|
|
[2]
|
Stechkin, S.R. (1954) On Best Approxima-tion of Given Classes of Functions by Arbitrary Polynomials. Uspekhi Matematicheskikh Nauk, 9, 133-134. (In Rus-sian)
|
|
[3]
|
Tikhomirov, V.M. (1960) Diameters of Sets in Function Spaces and the Theory of Best Approximations. Uspekhi Matematicheskikh Nauk, 15, 81-120.
|
|
[4]
|
Tikhomirov, V.M. (1969) Best Methods of Approximation of Dif-ferentiable Functions in the Space. Matematicheskii Sbornik, 80, 290-340.
|
|
[5]
|
Tikhomirov, V.M. (1976) Some Prob-lems in the Theory of Approximation. Nauka, Moscow.
|
|
[6]
|
Tikhomirov, V.M. (1990) Theory of Extremal Problems and Approximation Theory. Advances in Mathematics, 19, 449-451. (In Chinese)
|
|
[7]
|
Pietsch, A. (1974) s-Numbers of Operators in Banach Spaces. Studia Mathematica, No. 51, 201-223. [Google Scholar] [CrossRef]
|
|
[8]
|
Pinkus, A. (1985) n-Widths in Approximation Theory. Springer, Berlin.
|