Convergence Of Cascade Algorithms In Sobolev Spaces For Perturbed Refinement Masks

Abstract

. In this paper the convergence of the cascade algorithm in a Sobolev space is considered if the refinement mask is perturbed. It is proved that the cascade algorithm corresponding to a slightly perturbed mask converges. Moreover, the perturbation of the resulting limit function is estimated in terms of that of the masks. x1. Introduction In this paper we are concerned with the following problem: Given a compactly supported multivariate refinable function OE, how does perturbation of its finite refinement mask affect the convergence of the cascade algorithm? Further, if the cascade algorithm for the perturbed mask also converges, how the resulting limit function is related with OE? We say that a compactly supported function OE is M-refinable if it satisfies a refinement equation OE = X ff2ZZ s a(ff)OE(M \Delta \Gamma ff); (1:1) where the finitely supported sequence a = (a(ff)) ff2ZZ s is called the refinement mask. The s \Theta s matrix M is called a dilation matrix. We suppo..