Cardinal Interpolation with Gaussian Kernels

被引：0
作者：
T. Hangelbroek
W. Madych
F. Narcowich
J. D. Ward
机构：
[1] University of Connecticut Storrs,Department of Mathematics
[2] Texas A&M University,Department of Mathematics
来源：
Journal of Fourier Analysis and Applications | 2012年 / 18卷
关键词：
Interpolation; Gaussians; Shift-invariant spaces; Radial basis functions; Multipliers; 41A15; 41A25; 41A63; 42B15;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
In this paper, interpolation by scaled multi-integer translates of Gaussian kernels is studied. The main result establishes Lp Sobolev error estimates and shows that the error is controlled by the Lp 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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页码：67 / 86
页数：19
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