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On refinable functions and subdivision with positive masks

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Abstract

We consider aspects of the analysis of refinement equations with positive mask coefficients. First we derive, explicitly in terms of the mask, estimates for the geometric convergence rate of both the cascade algorithm and the corresponding subdivision scheme, as well as the Hölder continuity exponent of the resulting refinable function. Moreover, we show that the subdivision scheme converges for a class of unbounded initial sequences. Finally, we present a regularity result containing sufficient conditions on the mask for the refinable function to possess continuous derivatives up to a given order.

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Authors and Affiliations

  1. Department of Mathematics, University of Stellenbosch, Private Bag X1, Matieland, 7602, South Africa

    Johan De Villiers

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  1. Johan De Villiers
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Correspondence to Johan De Villiers.

Additional information

Communicated by T. Sauer

Dedicated to Charles Micchelli on his sixtieth birthday

Mathematics subject classifications (2000)

42C40, 65T60.

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De Villiers, J. On refinable functions and subdivision with positive masks. Adv Comput Math 24, 281–295 (2006). https://doi.org/10.1007/s10444-004-7628-x

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  • DOI: https://doi.org/10.1007/s10444-004-7628-x

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