一种广义周期Besov类的多元周期多项式样条逼近

APPROXIMATION BY PERIODIC POLYNOMIAL SPLINE FUNCTIONS FOR GENERALIZED PERIODIC BESOV CLASSES

本文证明多元多项式周期样条空间是某些多元周期光滑函数类的关于 Kolmogorovn 宽度的弱渐近极子空间. 给出了广义周期Besov类的一种推广,得到了空间元素的一种表示定理,不仅给出了一种多元周期多项式样条算子. 而且证明了所得的结果.

In this paper, We will prove that the space of multivariate periodic polynomial splines are weakly asymptotically optimal subspaces for the Kolmogorov widths of some multivariate periodic smoothness function classes. We give an extension of periodic Besov classes first. And then we obtain a kind of representation theorem for the elements in the periodic Besov classes, and we give a kind of multivariate periodic polynomial spline operators. At last we obtain our results by combining our operators and the representation theorem.