Constructional Approaches on Vector-valued Wavelets with Multi-scale Dilation Factor

摘要

In this work, the notion of vector-valued multiresolution analysis and biort-ogonal vector-valued wavelets is introduced. The existence of finitely supported biorthogonal vector-valued wavelets associated with a pair of biorthogonal finitely supported vector-valued scaling functions is investigated. A new method for construc-rn-ting a class of biorthogonal finitely supported vector-valued wavelet functions is presented by using multiresolution analysis and matrix theory. A sufficient condition for the existence of multiple pseudoframes for subspaces is derived