Séminaire de Probabilités

The Liouville theorem for Fourier multipliers

Name: The Liouville theorem for Fourier multipliers
Start: 2022-09-20T09:45:00+02:00
End: 2022-09-20T10:45:00+02:00
Location: Amphi Schwartz

par Prof. René Schilling (TU Dresden)

mardi 20 sept. 2022, 09:45 → 10:45 Europe/Paris

Amphi Schwartz

Description

We prove, for a class of nonlocal operators, the Liouville theorem, i.e.\ bounded harmonic functions are a.e. constant. For generators of Levy processes, we give even a necessary and sufficient criterium for the Liouville property. Extensions to strong Liouville and polynomial Liouvelle properties are given and the relation to coupling is discussed.