English

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 LpL_p Sobolev error estimates and shows that the error is controlled by the LpL_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<1<p<\infty, and involves a logarithmic term when p=1p=1 or \infty.

Keywords

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

R2 v1 2026-06-21T16:02:34.493Z