Nonseparable, Compactly Supported Interpolating Refinable Functions with Arbitrary Smoothness

In this paper we construct families of compactly supported nonseparable interpolating refinable functions with arbitrary smoothness (or regularity). The symbols for the newly constructed scaling functions are given by a simple formula related to the Bernstein polynomials. The emphasis of the paper i...

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Bibliographic Details
Published in:Applied and computational harmonic analysis 2001-03, Vol.10 (2), p.113-138
Main Author: Derado, Josip
Format: Article
Language:English
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Summary:In this paper we construct families of compactly supported nonseparable interpolating refinable functions with arbitrary smoothness (or regularity). The symbols for the newly constructed scaling functions are given by a simple formula related to the Bernstein polynomials. The emphasis of the paper is to show that under an easy-to-verify geometric condition these families satisfy Cohenrs condition, and they have arbitrarily high regularity. Furthermore, the constructed scaling functions satisfy, under the same geometrical condition, the Strang–Fix conditions of arbitrarily high order, which implies that corresponding interpolating schemes have arbitrarily high accuracy.
ISSN:1063-5203
1096-603X
DOI:10.1006/acha.2000.0334