Cardinal Interpolation with Gaussian Kernels Academic Article uri icon

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 ∞. © 2011 Springer Science+Business Media, LLC.

altmetric score

  • 2.5

author list (cited authors)

  • Hangelbroek, T., Madych, W., Narcowich, F., & Ward, J. D.

citation count

  • 15

publication date

  • June 2011