Spectral Approximation Orders of Multidimensional Nonstationary Biorthogonal Semi-Multiresolution Analysis in Sobolev Space

Spectral Approximation Orders of Multidimensional Nonstationary Biorthogonal Semi-Multiresolution Analysis in Sobolev Space

Year:    2006

Author:    Wensheng Chen, Xu Chen, Wei Lin

Journal of Computational Mathematics, Vol. 24 (2006), Iss. 1 : pp. 81–90

Abstract

Subdivision algorithm (Stationary or Non-stationary) is one of the most active and exciting research topics in wavelet analysis and applied mathematical theory. In multidimensional non-stationary situation, its limit functions are both compactly supported and infinitely differentiable. Also, these limit functions can serve as the scaling functions to generate the multidimensional non-stationary orthogonal or biorthogonal semi-multiresolution analysis (Semi-MRAs). The spectral approximation property of multidimensional non-stationary biorthogonal Semi-MRAs is considered in this paper. Based on nonstationary subdivision scheme and its limit scaling functions, it is shown that the multidimensional nonstationary biorthogonal Semi-MRAs have spectral approximation order $r$ in Sobolev space $H^s({\mathbb R}^d)$, for all $r\geq s\geq 0$.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/2006-JCM-8735

Journal of Computational Mathematics, Vol. 24 (2006), Iss. 1 : pp. 81–90

Published online:    2006-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    10

Keywords:    Nonstationary subdivision algorithm Biorthogonal Semi-MRAs Wavelets Spectral approximation Sobolev space.

Author Details

Wensheng Chen

Xu Chen

Wei Lin