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 .
CITATION STYLE
Jia, R.-Q. (1998). Approximation properties of multivariate wavelets. Mathematics of Computation, 67(222), 647–665. https://doi.org/10.1090/s0025-5718-98-00925-9
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