The Description of Characters of Matrix-Block Multielement Wavelet Wraps according to a Dilation Matrix

摘要

Wavelet analysis has become a developing branch of mathematics for over twenty years. In this paper, the notion of matrix-valued multiresolution analysis of space L~2(R~n ,C~(r×r)) is introduced. A method for constructing biorthogonal matrix-valued trivariate wavelet packets is developed and their properties are discussed by means of time-frequency analysis method, matrix theory and functional analysis method. Three biorthogonality formulas concerning these wavelet packets are provided. Finally, new Riesz bases of space L~2(R~n ,C~(r×r)) is obtained by constructing a series of subspaces of biorthogonal matrix-valued wavelet packets.