caa a22 4500 44586205X CHVBK 20180317145446.0 cr unu---uuuuu 170323e20110301xx s 000 0 eng 10.1007/s10092-010-0025-6 doi (NATIONALLICENCE)springer-10.1007/s10092-010-0025-6 Baxter B. Department of Economics, Mathematics and Statistics, Birkbeck College, University of London, Malet Street, London, WC1E 7HX, UK aut On kernel engineering via Paley-Wiener [Elektronische Daten] [B. Baxter] A radial basis function approximation takes the form $$s(x)=\sum_{k=1}^na_k\phi(x-b_k),\quad x\in {\mathbb{R}}^d,$$ where the coefficients a 1, ,a n are real numbers, the centres b 1, ,b n are distinct points in ℝd, and the function φ:ℝd→ℝ is radially symmetric. Such functions are highly useful in practice and enjoy many beautiful theoretical properties. In particular, much work has been devoted to the polyharmonic radial basis functions, for which φ is the fundamental solution of some iterate of the Laplacian. In this note, we consider the construction of a rotation-invariant signed (Borel) measure μ for which the convolution ψ=μ φ is a function of compact support, and when φ is polyharmonic. The novelty of this construction is its use of the Paley-Wiener theorem to identify compact support via analysis of the Fourier transform of the new kernel ψ, so providing a new form of kernel engineering. Springer-Verlag, 2010 Radial basis functions nationallicence Spherical average nationallicence Compact support nationallicence Paley-Wiener nationallicence Calcolo Springer Milan 48/1(2011-03-01), 21-31 0008-0624 48:1<21 2011 48 10092 https://doi.org/10.1007/s10092-010-0025-6 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10092-010-0025-6 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Baxter B. Department of Economics, Mathematics and Statistics, Birkbeck College, University of London, Malet Street, London, WC1E 7HX, UK aut NATIONALLICENCE 773 0- Calcolo Springer Milan 48/1(2011-03-01), 21-31 0008-0624 48:1<21 2011 48 10092 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer