Finitelly generated multiresolucion analysis in several variables

Abstract

Let r be a lattice in ]Rn and A a dilation matrix such that Ar e r. Let 'P be a localized square integrable vector function and assume that the lattice translates of 'P are orthonormal. We give necessary and sufficient conditions on 'P in order that it generates a Multiresolution Analysis in ]Rn with respect to the . lattice r and the dilation A. This characterization extends previous results to the case of regular non-compactly supported functions.