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 , 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 is based here on the identification of its dual with a certain space of multivariate polynomials. This point of view allows us to solve a class of multivariate interpolation problems by the polynomials from , with interpolation data characterized by the structure of , and to construct bases of corresponding to the interpolation problem.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1990-0956032-6

Keywords:
Box splines,
exponential box spline,
approximation order,
quasi-interpolants,
interpolation,
local approximation,
multivariate

Article copyright:
© Copyright 1990
American Mathematical Society