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).