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.
|Journal||Bulletin des Sciences Mathematiques|
|Number of pages||15|
|Publication status||Submitted - 2020|
- Fundamental Solutions
- Pseudo-Differential Equations