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Pointwise eigenfunction estimates and intrinsic ultracontractivity-type properties of Feynman-Kac semigroups for a class of levy processes
journal contribution
posted on 2016-05-27, 13:54 authored by Kamil Kaleta, Jozsef LorincziWe 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.
History
School
- Science
Department
- Mathematical Sciences
Published in
Annals of ProbabilityVolume
43Issue
3Pages
1350 - 1398Citation
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.Publisher
© Institute of Mathematical SciencesVersion
- VoR (Version of Record)
Publisher statement
This work is made available according to the conditions of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) licence. Full details of this licence are available at: https://creativecommons.org/licenses/by-nc-nd/4.0/Acceptance date
2013-10-14Publication date
2015-05-05Notes
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-AOP897ISSN
0091-1798eISSN
2168-894XPublisher version
Language
- en