Width And Optimal Recovery Theory

Over the past two decades, The theory on width and the optimal recovery of approximation have made a greatly development.Today,It has formed a relatively completely, with a very extensive set in the abstract space, the width of the order in the analysis of the completion of a number of fundamental significance in the function classes under a certain scale of the quantitative estimate of the width, including some very precise and detailed estimates, and in the solution to this problem, the approximation of the methods and techniques have been developed.This paper considers the width of the anisotropic Besov classes on periodic function with mixed norm,The width of the anisotropic Besov function is a new subject in classic function approximation. Because the Dirichlet and Vallee-Poussin kernel is not fit, so we reform the classic kernels and integret the transformation method of Fourier, We estimate the widths order of the new function class and have the accurate constant. In this paper, we consider the function in the case that P is different. We define a new discretization function and have new representation theorem.We have result as following: let...