Transactions of the American Mathematical Society

Characterization of Smoothness of Multivariate Refinable Functions in Sobolev Spaces

Author(s): Rong-Qing Jia
Journal: Trans. Amer. Math. Soc. 351 (1999), 4089-4112.
MSC (1991): Primary 42C15, 39B99, 46E35
Posted: July 1, 1999
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Abstract: Wavelets are generated from refinable functions by using multiresolution analysis. In this paper we investigate the smoothness properties of multivariate refinable functions in Sobolev spaces. We characterize the optimal smoothness of a multivariate refinable function in terms of the spectral radius of the corresponding transition operator restricted to a suitable finite dimensional invariant subspace. Several examples are provided to illustrate the general theory.

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Retrieve articles in Transactions of the American Mathematical Society with MSC (1991): 42C15, 39B99, 46E35

Rong-Qing Jia
Affiliation: Department of Mathematical Sciences, University of Alberta, Edmonton, Canada T6G 2G1
Email: jia@xihu.math.ualberta.ca

DOI: 10.1090/S0002-9947-99-02185-6
PII: S 0002-9947(99)02185-6
Keywords: Refinement equations, refinable functions, wavelets, smoothness, regularity, approximation order, Sobolev spaces, Lipschitz spaces, subdivision operators, transition operators
Received by editor(s): June 11, 1996
Received by editor(s) in revised form: April 14, 1997
Posted: July 1, 1999
Additional Notes: Supported in part by NSERC Canada under Grant OGP 121336
Copyright of article: Copyright 1999, American Mathematical Society

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