Séminaire de Probabilités

The Liouville theorem for Fourier multipliers

by Prof. René Schilling (TU Dresden)

Amphi Schwartz

Amphi Schwartz


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.