Construction of Orthonormal Multivariate Wavelets

Abstract

The purpose of this paper is to explain the construction of orthonormal multivariate wavelets associated with a multiresolution analysis. This paper primarily uses the work of R. A. Zalik [10], where he outlines a method of constructing orthonormal multivariate wavelets given an existing orthonormal multivariate wavelet associated with an MRA, and attempts to clarify it for a wider audience. In the last section, I use the result in constructing some orthonormal multivariate wavelets in various examples.