多元 Besov-Wiener 类的无穷维宽度和最优恢复

数学物理学报 ›› 2009, Vol. 29 ›› Issue (4): 1001-1011.

多元 Besov-Wiener 类的无穷维宽度和最优恢复

(天津师范大学数学科学学院, 天津 300387)

收稿日期:2007-02-26 修回日期:2008-03-08 出版日期:2009-08-25 发布日期:2009-08-25
基金资助:
国家自然科学基金(10471010)、天津师范大学教育基金(52LJ80)资助

Infinite-dimensional Widths and Optimal Recovery of Besov-Wiener Classes of Multivariate Functions

(College of Mathematical Science, Tianjin Normal University, Tianjin 300387)

Received:2007-02-26 Revised:2008-03-08 Online:2009-08-25 Published:2009-08-25
Supported by:
国家自然科学基金(10471010)、天津师范大学教育基金(52LJ80)资助

摘要/Abstract

摘要：

该文考虑 Besov-Wiener 类S_pqθ^r B(R^d)和 S_pqθ^r B(R^d)在 L_q(R^d) 空间下 (1≤ q ≤ p < ∞ ) 的无穷维 σ -宽度和最优恢复问题. 通过考虑样条函数逼近和构造一种连续样条算子, 得到了关于无穷维Kolmogorov 宽度、无穷维线性宽度、无穷维 Gel'fand 宽度和最优恢复的弱渐近结果.

关键词: Besov-Wiener 类, 无穷维宽度, 最优恢复

Abstract:

This paper concerns the problem of the infinite-dimensional σ-widths and optimal recovery of Besov-Wiener classes S_pqθ^r B(R^d) and S_pqθ^r B(R^d) in the metric L_q(R^d) for 1≤ q ≤ p < ∞. By considering the approximation by spline functions and constructing a kind of continuous spline operators, the author obtains the weak asymptotic results concerning the infinite dimensional Kolmogorov widths, the infinite dimensional linear widths, the infinite dimensional Gel'fand widths and optimal recovery, respectively.

Key words: Besov-Wiener classes, Infinite-dimensional width, Optimal recovery

中图分类号:

41A55

许贵桥. 多元 Besov-Wiener 类的无穷维宽度和最优恢复[J]. 数学物理学报, 2009, 29(4): 1001-1011.

HU Gui-Qiao. Infinite-dimensional Widths and Optimal Recovery of Besov-Wiener Classes of Multivariate Functions[J]. Acta mathematica scientia,Series A, 2009, 29(4): 1001-1011.