由Fourier系数确定的函数类的最佳m-项单边逼近渐近估计(英文)

The Asymptotic Estimations of Best m-term One-sided Approximation of Function Classes Determined by Fourier Coefficients

结合最佳m项逼近和单边逼近的思想引进所谓最佳m项单边逼近的概念,给出由Fourier系数确定的光滑函数类通过三角函数系在L_p(1≤p≤∞)的最佳m-项单边逼近渐近估计以及m-项类贪婪单边逼近结果.

In this paper a new kind of approximation method, called non-linear m-term onesided approximation, is introduced by combining the non-linear best m-term approximation with the one-sided approximation. With this new kind of approximation method, asymptotic estimates of nonlinear best m-term one-sided approximation, given by the trigonometric function system under the norm Lp （1 ≤p ≤∞） of function classes determined by Fourier coefficients, and corresponding m-term greedy-liked one-sided approximation results are given.