Compactly supported multi-wavelets

Abstract

In this paper we show some construction of compactly supported multi-wavelets In $L^2(\mathbb{R}^d)$, $d \geq 2$ which is based on the one-dimensional case, when $d = 1$. We also demonstrate that some methods, which are useful in the construction of wavelets with a compact support at $d = 1$, can be adapted to higher-dimensional cases if $A \in M_{d \times d}(\mathbb{Z})$ is an expansive matrix of a special form.