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

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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.

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Periodical:

Edited by:

Qi Luo

Pages:

1454-1459

DOI:

10.4028/www.scientific.net/AMM.58-60.1454

Citation:

H. L. Gao "The Orthogonality Characters of Multiple Vector-Valued Ternary Wavelets and Applications in Theoretical Physics", Applied Mechanics and Materials, Vols. 58-60, pp. 1454-1459, 2011

Online since:

June 2011

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$35.00

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