SPECTRAL APPROXIMATION ORDERS OF MULTIDIMENSIONAL NONSTATIONARY BIORTHOGONAL SEMI-MULTIRESOLUTION ANALYSIS IN SOBOLEV SPACE

• 来源期刊: 计算数学（英文版）
• 关键词: Nonstationary subdivision algorithm Biorthogonal Semi-MRAs Wavelets Spectral approximation Sobolev space.
• 年，卷（期）: 2006,（1）
• 页码范围: 81-90
• 页数: 10页
• 语种: 英文

摘要

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 nonstationary 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 Sobolevspace Hs(Rd), for all r ≥ s ≥ 0.