Decay of eigenfunctions and intrinsic ultracontractivity for Levy-Schroedinger operators

We consider the Feynman-Kac semigroups for a class of jump Levy processes satisfying some specific regularity conditions. Generators of these semigroups are sometimes called generalized Schroedinger operators. For these operators we present some new results on the behaviour of eigenfunctions at infinity. We also derive some characterization of intrinsic ultracontractivity given in terms of the corresponding Levy measures.
The talk is based on the joint paper with József Lorinczi (Loughborough University) available at arXiv:1209.4220.