多元Besov-Wiener类的无穷维宽度和最优恢复

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

该文考虑Besov-Wiener类S^r_(pqθ)B(R^d)和S^r_(pqθ)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.

This paper concerns the problem of the infinite-dimensional δ-widths and optimal recovery of Besov-Wiener classes S^rpqθB（R^d） and S^rqpθB（R^d） in the metric Lq（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 theinfinite dimensional Kolmogorov widths, the infinite dimensional linear widths, the infinite dimensional Gel＇land widths and optimal recovery, respectively.