TY - JOUR

T1 - Local approximation by certain spaces of exponential polynomials, approximation order of exponential box splines, and related interpolation problems

AU - Dyn, N.

AU - Ron, A.

PY - 1990/5

Y1 - 1990/5

N2 - Local approximation order to smooth complex valued functions by a finite dimensional space K, 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 K is based here on the identification of its dual with a certain space P of multivariate polynomials. This point of view allows us to solve a class of multivariate interpolation problems by the polynomials from P, with interpolation data characterized by the structure of K, and to construct bases of P corresponding to the interpolation problem.

AB - Local approximation order to smooth complex valued functions by a finite dimensional space K, 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 K is based here on the identification of its dual with a certain space P of multivariate polynomials. This point of view allows us to solve a class of multivariate interpolation problems by the polynomials from P, with interpolation data characterized by the structure of K, and to construct bases of P corresponding to the interpolation problem.

UR - http://www.scopus.com/inward/record.url?scp=0001467606&partnerID=8YFLogxK

U2 - 10.1090/S0002-9947-1990-0956032-6

DO - 10.1090/S0002-9947-1990-0956032-6

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AN - SCOPUS:0001467606

SN - 0002-9947

VL - 319

SP - 381

EP - 403

JO - Transactions of the American Mathematical Society

JF - Transactions of the American Mathematical Society

IS - 1

ER -