Approximation of functions by wavelet expansions with dilation matrix

Abstract

In this paper, we obtain the degree of approximation of a function f in Lp(1 ? p ? ?) norm under general conditions of the pointwise and uniform convergence of wavelet expansions associated with the multiresolution analysis with dilation matrix. Our results show that the degree has the exponential decay (faster than any polynomial) for the function f in Lp(R) on a finite interval (a, b).