MiS Preprint Repository

Delve into the future of research at MiS with our preprint repository. Our scientists are making groundbreaking discoveries and sharing their latest findings before they are published. Explore repository to stay up-to-date on the newest developments and breakthroughs.

MiS Preprint

On hypoellipticity of generators of Lévy processes

Helmut Abels and Ryad Husseini


We give a sufficient condition on a Lévy measure $\mu$ which ensures that the generator $L$ of the corresponding pure jump Lévy process is (locally) hypoelliptic, i.e., the singular support of $u$ is contained in the singular support of $Lu$ for all admissible $u$. In particular, we assume that $\mu$ is smooth away from the origin. We also show that this condition is necessary provided that the support of $\mu$ is compact.

Aug 14, 2008
Aug 25, 2008
MSC Codes:
35H10, 35S99, 47G20, 47G30, 60J75
L\'evy processes, L\'evy measures, hypoelliptic, convolution operators, integro-differential operators

Related publications

2010 Repository Open Access
Helmut Abels and Ryad Husseini

On hypoellipticity of generators of Lévy processes

In: Arkiv för matematik, 48 (2010) 2, pp. 231-242