Felipe Gonçalves, Michael Kelly, José Madrid
Published 2014-10-13Version 1
We construct majorants and minorants of a Gaussian function in Euclidean space that have Fourier transforms supported in a box. The majorants that we construct are shown to be extremal and our minorants are shown to be asymptotically extremal as the sides of the box become uniformly large. We then adapt the Distribution and Gaussian Subordination methods of Carneiro-Littmann-Vaaler to the multidimensional setting to obtain majorants and minorants for a class of radial functions. Periodic analogues of the main results are proven and applications to Hilbert-type inequalities are given.
On approximations by shifts of the Gaussian function
Extremal functions in de Branges and Euclidean spaces
On the Gaussian functions of two discrete variables
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