MiS Preprint Repository

We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV ( that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

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.

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