TY - JOUR
T1 - Spectral Approximation Orders of Multidimensional Nonstationary Biorthogonal Semi-Multiresolution Analysis in Sobolev Space
AU - Chen , Wensheng
AU - Chen , Xu
AU - Lin , Wei
JO - Journal of Computational Mathematics
VL - 1
SP - 81
EP - 90
PY - 2006
DA - 2006/02
SN - 24
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/jcm/8735.html
KW - Nonstationary subdivision algorithm, Biorthogonal Semi-MRAs, Wavelets,
Spectral approximation, Sobolev space.
AB - <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>