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.
