On the Liouville and strong Liouville properties for a class of non-local operators


  • David Berger
  • René L. Schilling




We prove a necessary and sufficient condition for the Liouville and strong Liouville properties of the infinitesimal generator of a Lévy process and subordinate Lévy processes. Combining our criterion with the necessary and sufficient condition obtained by Alibaud et al., we obtain a characterization of (orthogonal subgroup of) the set of zeros of the characteristic exponent of the Lévy process.


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How to Cite

Berger, D., & Schilling, R. L. (2022). On the Liouville and strong Liouville properties for a class of non-local operators. MATHEMATICA SCANDINAVICA, 128(2). https://doi.org/10.7146/math.scand.a-132068