Diverse Smooth Periodic Function M Approximation

This paper is devoted to nonlinear approximation ,namely,m-term approximtion of anisotropic smooth periodic functions.Nonlinear approximation is the important part of approximation the-ory.It means that the approximants do not come from linear spaces but rather from nonlinear manifolds.The advantages of nonlinear approximation show that one can achieve a given accuracy of approximation while assuming less smoothness on the function in the nonlinear case than is necessary in the corresponding linear approximation.Nonlinear approximation is used significantly in many applications,such as image processing ,noise removal and the solution of operation equations and so on.In chapter I we obtain the rate of m-term approximation of the anisotropic class Sobolev and Nikol'skii. In chapter II we give the representation theorem of the anisotropic class Besov and get the estimation of m-term approximation of it .In chaper III the rate of m-term approximation of the anisotropic low smooth class is camputated .