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

Hai Lin Gao

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

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HomeApplied Mechanics and MaterialsApplied Mechanics and Materials Vols. 58-60The Orthogonality Characters of Multiple...

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, C^r^×^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, C^r^×^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:

Applied Mechanics and Materials (Volumes 58-60)

Pages:

1454-1459

DOI:

https://doi.org/10.4028/www.scientific.net/AMM.58-60.1454

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Online since:

June 2011

Authors:

Hai Lin Gao

Keywords:

Besov Space, Integer-Valued Dilation Matrix, Iteration Procedure, Multiple Vector-Valued Wavelets, Orthonormal Wavelet Wrap Base, Wavelet Wrap

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