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Mathematics of Computation

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Approximation properties of multivariate wavelets

Author: Rong-Qing Jia
Journal: Math. Comp. 67 (1998), 647-665
MSC (1991): Primary 41A25, 41A63; Secondary 42C15, 65D15
MathSciNet review: 1451324
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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 $W_{1}^{k-1}(\mathbb {R}^{s})$ provides approximation order $k$.

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Additional Information

Rong-Qing Jia
Affiliation: Department of Mathematical Sciences, University of Alberta, Edmonton, Alberta, Canada T6G 2G1

Keywords: Refinement equations, refinable functions, wavelets, accuracy, approximation order, smoothness, subdivision operators, transition operators
Received by editor(s): April 17, 1996
Additional Notes: Supported in part by NSERC Canada under Grant OGP 121336.
Article copyright: © Copyright 1998 American Mathematical Society