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Local approximation by certain spaces of exponential polynomials, approximation order of exponential box splines, and related interpolation problems

Authors: N. Dyn and A. Ron
Journal: Trans. Amer. Math. Soc. 319 (1990), 381-403
MSC: Primary 41A15
MathSciNet review: 956032
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Abstract: Local approximation order to smooth complex valued functions by a finite dimensional space $ \mathcal{H}$, spanned by certain products of exponentials by polynomials, is investigated. The results obtained, together with a suitable quasi-interpolation scheme, are used for the derivation of the approximation order attained by the linear span of translates of an exponential box spline.

The analysis of a typical space $ \mathcal{H}$ is based here on the identification of its dual with a certain space $ \mathcal{P}$ of multivariate polynomials. This point of view allows us to solve a class of multivariate interpolation problems by the polynomials from $ \mathcal{P}$, with interpolation data characterized by the structure of $ \mathcal{H}$, and to construct bases of $ \mathcal{P}$ corresponding to the interpolation problem.

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Keywords: Box splines, exponential box spline, approximation order, quasi-interpolants, interpolation, local approximation, multivariate
Article copyright: © Copyright 1990 American Mathematical Society

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