@inbook{4998e7f75a5f4b3ca1ecd72c2a2de254,

title = "The discrete analog of the Malgrange-Ehrenpreis theorem",

abstract = "One of the landmarks of the modern theory of partial differential equations is theMalgrange-Ehrenpreis theorem that states that every nonzero 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.",

keywords = "Formal Laurent series, Fundamental solution, Systems of constantcoefficient partial differential equations",

author = "Doron Zeilberger",

note = "Funding Information: I{\textquoteright}d like to thank an anonymous referee, and Hershel Farkas, for insightful comments. Accompanied by Maple package LEON available from http://www.math.rutgers.edu/\~zeilberg/tokhniot/LEON . Supported in part by the USA National Science Foundation.",

year = "2013",

doi = "10.1007/978-1-4614-4075-8_27",

language = "English (US)",

isbn = "9781461440741",

series = "Developments in Mathematics",

pages = "537--541",

editor = "Hershel Farkas and Marvin Knopp and Robert Gunning and B.A Taylor",

booktitle = "From Fourier Analysis and Number Theory to Radon Transforms and Geometry",

}