The Characterization of Biorthogonal Multidimensional Vector Wavelet Wraps with Nine-Scale Dilation Factor

Zong Sheng Sheng; Yu Min Yu

doi:10.4028/www.scientific.net/AMR.171-172.121

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HomeAdvanced Materials ResearchAdvanced Materials Research Vols. 171-172The Characterization of Biorthogonal...

The Characterization of Biorthogonal Multidimensional Vector Wavelet Wraps with Nine-Scale Dilation Factor

Abstract:

Wavelet analysis is nowadays a widely used tool in applied mathematics. The advantages of wavelet wraps and their promising features in various application have attracted a lot of interest and effort in recent years. In this paper, we develop the notion of a sort of multivariate vector wavelet wraps. A new approcah for designing the multidimensional vector wavelet wraps is formul- ated. Their characters are investigated by virtue of iterative method, time-frequency analysis metho- d and matrix theory. There biorthogonality formulas regarding the wavelet wraps are provided. Biorthogonality decomposition relation formulas of the space L2(Rn)r are obtained by constructing a series of subspaces of the vector-valued wavelet wraps. Moreover, several Riesz bases of space L2(Rn)r are constructed from the wavelet wraps.

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Periodical:

Advanced Materials Research (Volumes 171-172)

Pages:

121-124

DOI:

https://doi.org/10.4028/www.scientific.net/AMR.171-172.121

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Online since:

December 2010

Authors:

Zong Sheng Sheng, Yu Min Yu

Keywords:

Biorthogonality Formula, Iterative Method, Multidimensional, Riesz Base, Tight Wavelet Frames, Vector Scaling Function, Vector Wavelet Wraps

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