Spectral Models for Orthonormal Wavelets and Multiresolution Analysis of $L^2({\mathbb R})$

Abstract

Spectral representations of the dilation and translation operators on $L^2({\mathbb R})$ are built through appropriate bases. Orthonormal wavelets and multiresolution analysis are then described in terms of rigid operator-valued functions defined on the functional spectral spaces. The approach is useful for computational purposes.