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[Appeared in: "From Fourier Analysis and Number Theory to Radon Transforms and Geometry-In Memory of Leon Ehrenpreis"
(Developments in Mathematics)
edited by M. Farkas, R. C. Gunning, Marvin I. Knopp z"l, and B.A. Taylor, Springer, published Sept. 2012]

In fond memory of Leon Ehrenpreis (1930-2010)

Written: July 21, 2011

One of the landmarks of the modern theory of partial differential equations is the Malgrange-
Ehrenpreis theorem that states that every non-zero linear partial differential
operator with constant coefficients has a Green function (alias fundamental solution).
In this short note I state the discrete analog, and give two proofs. The first one is Ehrenpreis-
style, using duality, and the second one is constructive, using formal Laurent series.
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