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.