Year: 1998
Type: article
Abstract: Wavelets are generated from refinable functions by using multiresolution analysis. In this paper we investigate the approximation properties of multivariate refinable functions. We give a characterization for the approximation order provided by a refinable function in terms of the order of the sum rules satisfied by the refinement mask. We connect the approximation properties of a refinable function with the spectral properties of the corresponding subdivision and transition operators. Finally, we demonstrate that a refinable function in W 1 k − 1 ( R s ) W_{1}^{k-1}(\mathbb {R}^{s}) provides approximation order k k .
Source: Mathematics of Computation
Author: Rong-Qing Jia
Institution: University of Alberta
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: bronze
OpenAlex ID: W1971998705