Equations For Frame Wavelets In $L^2(\R^2)$

TL;DR

This paper derives a system of equations characterizing single function normalized tight frame wavelets with compact support in two-dimensional space, linked to expansive integer matrices.

Contribution

It introduces a new set of equations for constructing tight frame wavelets in $L^2( ^2)$ associated with $2\times 2$ matrices, advancing wavelet theory.

Findings

Derived equations for tight frame wavelets in $L^2( ^2)$

Connected wavelet properties to expansive integer matrices

Provided a mathematical framework for wavelet construction

Abstract

We establish system of equations for single function normalized tight frame wavelets with compact supports associated with $2\times 2$ expansive integral matrices in $L^2(\R^2)$.