A Study of a Two-Directional Vector Multivariate Wavelet Wraps and Applications in Engineering Materials

Jin Shun Feng; Qing Jiang Chen

doi:10.4028/www.scientific.net/AMR.889-890.1270

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HomeAdvanced Materials ResearchAdvanced Materials Research Vols. 889-890A Study of a Two-Directional Vector Multivariate...

A Study of a Two-Directional Vector Multivariate Wavelet Wraps and Applications in Engineering Materials

Abstract:

The existence of compactly supported orthogonal two-directional vector-valued wavelets associated with a pair of orthogonal shortly supported vector-valued scaling functions is researched. We introduce a class of two-directional vector-valued four-dimensional wavelet wraps according to a dilation matrix, which are generalizations of univariate wavelet wraps. Three orthogonality formulas regarding the wavelet wraps are established. Finally, it is shown how to draw new Riesz bases of space from these wavelet wraps. The sufficient condition for the existence of four-dimensional wavelet wraps is established based on the multiresolution analysis method.

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Periodical:

Advanced Materials Research (Volumes 889-890)

Pages:

1270-1274

DOI:

https://doi.org/10.4028/www.scientific.net/AMR.889-890.1270

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Online since:

February 2014

Authors:

Jin Shun Feng, Qing Jiang Chen

Keywords:

Affine Frames, Parseval Frames, Quarternary, Two-Directional Scaling Function, Two-Directional Wavelets, Vector Space, Vector Subdivision Scheme, Vector-Valued Wavelet Wraps

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References

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