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Approximation order provided by refinable function vectors

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Abstract

In this paper we considerL p-approximation by integer translates of a finite set of functionsϕ v (v=0, ...,r − 1) which are not necessarily compactly supported, but have a suitable decay rate. Assuming that the function vectorϕ=(ϕ =0/ r−1 is refinable, necessary and sufficient conditions for the refinement mask are derived. In particular, if algebraic polynomials can be exactly reproduced by integer translates ofϕ v, then a factorization of the refinement mask ofϕ can be given. This result is a natural generalization of the result for a single functionϕ, where the refinement mask ofϕ contains the factor ((1 +e −iu)/2)m if approximation orderm is achieved.

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Authors and Affiliations

  1. Fachbereich Mathematik, Universität Rostock, D-18051, Rostock, Germany

    G. Plonka

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  1. G. Plonka
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Communicated by Carl de Boor.

Dedicated to Professor L. Berg on the occasion of his 65th birthday

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Plonka, G. Approximation order provided by refinable function vectors. Constr. Approx 13, 221–244 (1997). https://doi.org/10.1007/BF02678465

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  • DOI: https://doi.org/10.1007/BF02678465

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