caa a22 4500 469068965 CHVBK 20180323132916.0 cr unu---uuuuu 170328e19920201xx s 000 0 eng 10.1007/BF02801574 doi (NATIONALLICENCE)springer-10.1007/BF02801574 On multivariate approximation by integer translates of a basis function [Elektronische Daten] [N. Dyn, I. Jackson, D. Levin, A. Ron] Approximation properties of the dilations of the integer translates of a smooth function, with some derivatives vanishing at infinity, are studied. The results apply to fundamental solutions of homogeneous elliptic operators and to "shifted” fundamental solutions of the iterated Laplacian. Following the approach from spline theory, the question of polynomial reproduction by quasi-interpolation is addressed first. The analysis makes an essential use of the structure of the generalized Fourier transform of the basis function. In contrast with spline theory, polynomial reproduction is not sufficient for the derivation of exact order of convergence by dilated quasi-interpolants. These convergence orders are established by a careful and quite involved examination of the decay rates of the basis function. Furthermore, it is shown that the same approximation orders are obtained with quasi-interpolants defined on a bounded domain. The Magnes Press, 1992 Dyn N. School of Mathematical Sciences, Sackler Faculty of Exact Sciences, Tel Aviv University, Tel Aviv, Israel aut Jackson I. Department of Applied Mathematics and Theoretical Physics, Cambridge University, Cambridge, England aut Levin D. School of Mathematical Sciences, Sackler Faculty of Exact Sciences, Tel Aviv University, Tel Aviv, Israel aut Ron A. Computer Sciences Department, University of Wisconsin-Madison, 53706, Madison, WI, USA aut Israel Journal of Mathematics Springer-Verlag 78/1(1992-02-01), 95-130 0021-2172 78:1<95 1992 78 11856 https://doi.org/10.1007/BF02801574 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF02801574 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Dyn N. School of Mathematical Sciences, Sackler Faculty of Exact Sciences, Tel Aviv University, Tel Aviv, Israel aut NATIONALLICENCE 700 1- Jackson I. Department of Applied Mathematics and Theoretical Physics, Cambridge University, Cambridge, England aut NATIONALLICENCE 700 1- Levin D. School of Mathematical Sciences, Sackler Faculty of Exact Sciences, Tel Aviv University, Tel Aviv, Israel aut NATIONALLICENCE 700 1- Ron A. Computer Sciences Department, University of Wisconsin-Madison, 53706, Madison, WI, USA aut NATIONALLICENCE 773 0- Israel Journal of Mathematics Springer-Verlag 78/1(1992-02-01), 95-130 0021-2172 78:1<95 1992 78 11856 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer