Polynomial interpolation, ideals and approximation order of multivariate refinable functions

Sauer, Thomas

doi:10.1090/S0002-9939-02-06678-9

Polynomial interpolation, ideals and approximation order of multivariate refinable functions
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Proc. Amer. Math. Soc. 130 (2002), 3335-3347 Request permission

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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