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Title: Pointwise eigenfunction estimates and intrinsic ultracontractivity-type properties of Feynman-Kac semigroups for a class of levy processes
Authors: Kaleta, Kamil
Lorinczi, Jozsef
Issue Date: 2015
Publisher: © Institute of Mathematical Sciences
Citation: KALETA, K. and LORINCZI, J., 2015. Pointwise eigenfunction estimates and intrinsic ultracontractivity-type properties of Feynman-Kac semigroups for a class of levy processes. Annals of Probability, 43(3), pp. 1350-1398.
Abstract: We introduce a class of L´evy processes subject to specific regularity conditions, and consider their Feynman–Kac semigroups given under a Kato-class potential. Using new techniques, first we analyze the rate of decay of eigenfunctions at infinity.We prove bounds on - subaveraging functions, from which we derive two-sided sharp pointwise estimates on the ground state, and obtain upper bounds on all other eigenfunctions. Next, by using these results, we analyze intrinsic ultracontractivity and related properties of the semigroup refining them by the concept of ground state domination and asymptotic versions. We establish the relationships of these properties, derive sharp necessary and sufficient conditions for their validity in terms of the behavior of the L´evy density and the potential at infinity, define the concept of borderline potential for the asymptotic properties and give probabilistic and variational characterizations. These results are amply illustrated by key examples.
Description: This paper was published in the journal Annals of Probability and the definitive published version is available at http://dx.doi.org/10.1214/13-AOP897
Version: Published
DOI: 10.1214/13-AOP897
URI: https://dspace.lboro.ac.uk/2134/21398
Publisher Link: http://dx.doi.org/10.1214/13-AOP897
ISSN: 0091-1798
Appears in Collections:Published Articles (Maths)

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