LEON a Maple package for implementing some of the brilliant insights of Leon Ehrepreis (1930-2010). It accompanies the lecture given in Ehrenpreis’ memory. [Added July 21, 2011: it also accompanies the article written in Leon’s memory]. 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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  1. Zeilberger, Doron: The discrete analog of the Malgrange-Ehrenpreis theorem (2013)