@Article{JCM-24-1,
author = {Wensheng, Chen and Xu, Chen and Wei, Lin},
title = {Spectral Approximation Orders of Multidimensional Nonstationary Biorthogonal Semi-Multiresolution Analysis in Sobolev Space},
journal = {Journal of Computational Mathematics},
year = {2006},
volume = {24},
number = {1},
pages = {81--90},
abstract = {<p style="text-align: justify;">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 $r\geq s\geq 0$.</p>},
issn = {1991-7139},
doi = {https://doi.org/2006-JCM-8735},
url = {https://global-sci.com/article/85057/spectral-approximation-orders-of-multidimensional-nonstationary-biorthogonal-semi-multiresolution-analysis-in-sobolev-space}
}