Cardinal Interpolation with Gaussian Kernels |
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Authors: | T Hangelbroek W Madych F Narcowich J D Ward |
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Institution: | 2. Department of Mathematics, Texas A&M University, College Station, TX, 77843, USA 1. Department of Mathematics, University of Connecticut Storrs, Storrs, CT, 06269, USA
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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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Keywords: | |
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