The Characteristics of Trivariate Vector-Valued Super-Wave Wraps and Applications in Materials Engineering

Yong Yi Huang

doi:10.4028/www.scientific.net/AMR.915-916.1062

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HomeAdvanced Materials ResearchAdvanced Materials Research Vols. 915-916The Characteristics of Trivariate Vector-Valued...

The Characteristics of Trivariate Vector-Valued Super-Wave Wraps and Applications in Materials Engineering

Abstract:

The rise of wavelet analysis in applied mathematics is due to its applications and the flex- ibility. We introduce vector-valued wave wraps with multi-scale dilation factor for space , which is the generalization of univariate wavelet packets. A method for constructing a sort of orthogo-nal vector-valued wavelet wraps in three-dimensional space is presented and their orthogonality traits are characterized by virtue of iteration method and time-frequency analysis method. The orthog-onality formulas concerning these wave packets are established. Moreover, it is shown how to obtain new Riesz bases of space from these wave wraps. The notion of multiple pseudo fames for subspaces with integer translation is proposed. The construction of a generalized multiresolution structure of Paley-Wiener subspaces of is investigated. The pyramid decomposition scheme is derived based on a generalized multiresolution structure.

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Periodical:

Advanced Materials Research (Volumes 915-916)

Pages:

1062-1065

DOI:

https://doi.org/10.4028/www.scientific.net/AMR.915-916.1062

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Online since:

April 2014

Authors:

Yong Yi Huang*

Keywords:

Multiple Subspace Pseudofames, Orthogonality Formulas, Time-Frequency Analysis Method, Trivariate Wavelet Wraps, Vector-Valued Wave-Lets

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