Multivariate Refinable Functions of High Approximation Order Via Quotient Ideals of Laurent Polynomials |
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| Authors: | Mö ller,H. Michael,Sauer, Thomas |
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| Affiliation: | (1) FB Mathematik, Universität Dortmund, Vogelpothsweg 87, D-44221 Dortmund, Germany;(2) Lehrstuhl für Numerische Mathematik, Justus-Liebig-Universität Gießen, Heinrich-Buff-Ring 44, D-35392 Gießen, Germany |
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| Abstract: | We give an algebraic interpretation of the well-known  zero-condition or sum rule for multivariate refinable functions with respect to an arbitrary scaling matrix. The main result is a characterization of these properties in terms of containment in a quotient ideal, however not in the ring of polynomials but in the ring of Laurent polynomials. |
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| Keywords: | subdivision quotient ideals Laurent polynomials Grö bner bases |
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