The Orthogonality Characters of Multiple Vector-Valued Ternary Wavelets and Applications in Theoretical Physics

Abstract

Wavelet analysis has been the focus of active research for twenty years, both in theory and applications. In this work, we develop the concept of a class of multiple vector-valued trivariate wavelet wraps with a dilation matrix. A new method for constructing multiple vector-valued trivariate wavelet wraps is proposed. Their characters are investigated by means of operator technique, time-frequency analysis method and matrix theory. There orthogonality formulas regarding the wavelet wraps are provided. Orthogonality decomposition relation formulas of the space L2(R3, Cr×r)are obtained by constructing a series of subspaces of the multiple vector-valued wavelet wraps. Furthermore, several orthonormal wavelet wrap bases of space L2(R3, Cr×r) are constructed from the wavelet wraps. The pyramid decomposition scheme is obtained based on such a GMS and a sufficient condition for its existence is provided. Relation to theoretical physics is also discussed.