Cardinal Interpolation with Gaussian Kernels Academic Article

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.

authors

• Narcowich, Francis
• Ward, Joseph

published proceedings

• JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS

altmetric score

• 2.5

author list (cited authors)

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

citation count

• 17

complete list of authors

• Hangelbroek, T||Madych, W||Narcowich, F||Ward, JD

publication date

• February 2012

publisher

• Springer Nature  Publisher

published in

• Journal of Fourier Analysis and Applications  Journal

keywords

• Gaussians
• Interpolation
• Multipliers
• Radial Basis Functions
• Shift-invariant Spaces

Digital Object Identifier (DOI)

• 10.1007/s00041-011-9185-2

start page

• 67

end page

• 86

volume

• 18

issue

• 1

URL

• http%3A%2F%2Fdx.doi.org%2F10.1007%2Fs00041-011-9185-2