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Title: Characterization of compactly supported refinable splines
Authors: Lawton, W. 
Lee, S.L. 
Shen, Z. 
Keywords: AMS subject classification: 41A15, 41A30, 65D07
Refinable spline
Riesz basis
Issue Date: Jan-1995
Citation: Lawton, W.,Lee, S.L.,Shen, Z. (1995-01). Characterization of compactly supported refinable splines. Advances in Computational Mathematics 3 (1-2) : 137-145. ScholarBank@NUS Repository.
Abstract: We prove that a compactly supported spline function φ of degree k satisfies the scaling equation {Mathematical expression} for some integer m ≥ 2, if and only if {Mathematical expression} where p(n) are the coefficients of a polynomial P(z) such that the roots of P(z)(z - 1)k+1 TM are mapped into themselves by the mapping z →zm, and Bk is the uniform B-spline of degree k. Furthermore, the shifts of φ form a Riesz basis if and only if P is a monomial. © 1995 J.C. Baltzer AG, Science Publishers.
Source Title: Advances in Computational Mathematics
ISSN: 10197168
DOI: 10.1007/BF03028364
Appears in Collections:Staff Publications

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