## Approximation properties of multivariate wavelets

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- Math. Comp.
**67**(1998), 647-665 Request permission

## 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 $k$.## References

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## Additional Information

**Rong-Qing Jia**- Affiliation: Department of Mathematical Sciences, University of Alberta, Edmonton, Alberta, Canada T6G 2G1
- Email: jia@xihu.math.ualberta.ca
- Received by editor(s): April 17, 1996
- Additional Notes: Supported in part by NSERC Canada under Grant OGP 121336.
- © Copyright 1998 American Mathematical Society
- Journal: Math. Comp.
**67**(1998), 647-665 - MSC (1991): Primary 41A25, 41A63; Secondary 42C15, 65D15
- DOI: https://doi.org/10.1090/S0025-5718-98-00925-9
- MathSciNet review: 1451324