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

TL;DR

This paper develops spectral representations of dilation and translation operators on L^2(R), enabling a new approach to orthonormal wavelets and multiresolution analysis that is computationally advantageous.

Contribution

It introduces a spectral framework for wavelets and multiresolution analysis using operator-valued functions on spectral spaces, offering a novel computational perspective.

Findings

Spectral representations of dilation and translation operators are constructed.

Orthonormal wavelets are characterized via operator-valued functions.

The approach facilitates computational applications in wavelet analysis.

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.