Cardinal Interpolation with Gaussian Kernels
Classical Analysis and ODEs
2012-07-04 v1
Abstract
In this paper, interpolation by scaled multi-integer translates of Gaussian kernels is studied. The main result establishes Sobolev error estimates and shows that the error is controlled by the 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 , and involves a logarithmic term when or .
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Cite
@article{arxiv.1008.3168,
title = {Cardinal Interpolation with Gaussian Kernels},
author = {Thomas Hangelbroek and Wolodymyr Madych and F. J. Narcowich and J. D. Ward},
journal= {arXiv preprint arXiv:1008.3168},
year = {2012}
}
Comments
18 pages