The discrete analog of the Malgrange-Ehrenpreis theorem

Research output: Chapter in Book/Report/Conference proceedingChapter

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.

Original languageEnglish (US)
Title of host publicationFrom Fourier Analysis and Number Theory to Radon Transforms and Geometry
Subtitle of host publicationIn Memory of Leon Ehrenpreis
EditorsHershel Farkas, Marvin Knopp, Robert Gunning, B.A Taylor
Pages537-541
Number of pages5
DOIs
StatePublished - 2013

Publication series

NameDevelopments in Mathematics
Volume28
ISSN (Print)1389-2177

All Science Journal Classification (ASJC) codes

  • General Mathematics

Keywords

  • Formal Laurent series
  • Fundamental solution
  • Systems of constantcoefficient partial differential equations

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