Fundamental solutions to elliptic multipliers with real-analytic symbol in Rn

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Abstract

Using a version of Hironaka’s resolution of singularities for real-analytic functions, we show that any elliptic multiplier with real-analytic symbol has a tempered fundamental solution, and this can be weak∗-approximated by entire functions belonging to a certain Paley-Wiener space. In some special cases of global symmetry, the construction can be specialized to become fully explicit. We use this to compute tempered fundamental solutions for sums of powers of the Laplacian on Rn.
Original languageEnglish
JournalBulletin des Sciences Mathematiques
Number of pages15
ISSN0007-4497
Publication statusSubmitted - 2020

Keywords

  • Fundamental Solutions
  • Pseudo-Differential Equations
  • PDE

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