The (strong) Liouville property for a class of non-local operators
Abstract
We prove a necessary and sufficient condition for the Liouville and strong Liouville properties of the infinitesimal generator of a L\'evy process and subordinate L\'evy 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 L\'evy process.
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