Construction of a Class of Compactly Supported Biorthogonal Multiple Vector-Valued Wavelets

In this paper, we introduce the notion of vector-valued multiresolution analysis. We discuss the existence of biorthogonal multiple vector-valued wavelets. An algorithm for constructing a class of compactly supported biorthogonal multiple vector-valued wavelets associated with the biorthogonal multiple vector-valued scaling functions is presented by using multiresolution analysis and matrix theory.