On Riesz wavelets associated with multiresolution analyses

Abstract

We obtain some properties that Riesz wavelets and the corresponding scaling functions should satisfy in order that the Riesz wavelets be associated with multiresolution analyses (MRAs). They are given in terms of the low/high-pass filters and in terms of the Fourier transform by using the newly obtained necessary and sufficient condition for the sum of two principal shift-invariant subspaces to be closed. The properties are used to improve the characterizations of Riesz wavelets associated with MRAs previously obtained by some of the authors. (C) 2002 Elsevier Science (USA). All rights reserved.