The Discrete Analog of the Malgrange-Ehrenpreis Theorem

2011/07/21 by Doron Zeilberger, Zeilberger, Doron
Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #math.CO

paper · pdf · doi:10.48550/arxiv.1107.4380

4 pages. Articles written in fond memory of Leon Ehrenpreis (1930-2010)

arxiv created 2011/07/21 · arxiv updated 2011/07/25

Abstract

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. This article is accompanied by the Maple package LEON available from: http://www.math.rutgers.edu/~zeilberg/tokhniot/LEON .

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