Cardinal Interpolation with Gaussian Kernels

2010/08/18 by Thomas Hangelbroek, Wolodymyr Madych, F. J. Narcowich +1 · 1 citation
Mathematics · #math.CA #msc:41A15 #msc:41A25 #msc:41A63 #msc:42B15

paper · pdf · doi:10.1007/s00041-011-9185-2

published as Journal of Fourier Analysis and Applications: Volume 18, Issue 1 (2012), Page 67-86 · 18 pages

arxiv created 2010/08/18 · arxiv updated 2012/07/04

Abstract

In this paper, interpolation by scaled multi-integer translates of Gaussian kernels is studied. The main result establishes L_p Sobolev error estimates and shows that the error is controlled by the L_p multiplier norm of a Fourier multiplier closely related to the cardinal interpolant, and comparable to the Hilbert transform. Consequently, its multiplier norm is bounded independent of the grid spacing when 1<p<∞, and involves a logarithmic term when p=1 or ∞.

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• Minimal-Norm Extensions of Stationary Kernels on Subgroups of Locally Compact Abelian Groups and Gaussian Conditioning