On the Liouville and strong Liouville properties for a class of non-local operators
DOI:
https://doi.org/10.7146/math.scand.a-132068Abstract
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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