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Polynomial interpolation, ideals and approximation order of multivariate refinable functions


Author: Thomas Sauer
Journal: Proc. Amer. Math. Soc. 130 (2002), 3335-3347
MSC (2000): Primary 42C40, 13P10; Secondary 41A05
DOI: https://doi.org/10.1090/S0002-9939-02-06678-9
Published electronically: May 29, 2002
MathSciNet review: 1913013
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Abstract: The paper identifies the multivariate analog of factorization properties of univariate masks for compactly supported refinable functions, that is, the ``zero at $\pi$''-property, as containment of the mask polynomial in an appropriate quotient ideal. In addition, some of these quotient ideals are given explicitly.


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Additional Information

Thomas Sauer
Affiliation: Lehrstuhl für Numerische Mathematik, Justus–Liebig–Universität Gießen, Heinrich–Buff–Ring 44, D–35392 Gießen, Germany
Email: Tomas.Sauer@math.uni-giessen.de

DOI: https://doi.org/10.1090/S0002-9939-02-06678-9
Keywords: Subdivision, polynomial preservation, refinable functions, quotient ideals
Received by editor(s): October 26, 2000
Received by editor(s) in revised form: June 19, 2001
Published electronically: May 29, 2002
Additional Notes: This work was supported by Deutsche Forschungsgemeinschaft with a Heisenberg fellowship, Grant # Sa 627/6–1
Dedicated: Dedicated to C. A. Micchelli on the occasion of his 60th birthday, with friendship and gratitude for a wonderful collaboration.
Communicated by: David R. Larson
Article copyright: © Copyright 2002 American Mathematical Society

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