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Title: Spectral and analytic properties of some non-local Schrödinger operators and related jump processes
Authors: Lorinczi, Jozsef
Kaleta, Kamil
Durugo, Samuel O.
Keywords: Levy processes
Non-local Schrodinger operators
Feynman-Kac semigroups
Spectral properties
Decay of eigenfunctions
Lieb-Thirring inequality
Issue Date: 2015
Publisher: Società Italiana di Matematica Applicata e Industriale (SIMAI)
Citation: LORINCZI, J., KALETA, K. and DURUGO, S.O., 2015. Spectral and analytic properties of some non-local Schrödinger operators and related jump processes. Communications in Applied and Industrial Mathematics, 6 (2), e-534.
Abstract: We discuss recent developments in the spectral theory of non-local SchrOdinger operators via a Feynman-Kac-type approach. The processes we consider are subordinate Brownian motion and a class of jump Levy processes under a Kato-class potential. We discuss some explicitly soluble specific cases, and address the spatial decay properties of eigenfunctions and the number of negative eigenvalues in the general framework of the processes we introduce.
Description: This is an open access article published by the Italian Society for Applied and Industrial Mathematics (SIMAI)and licensed under the terms of the Creative Commons Attribution NonCommercial NoDerivs 3.0 License.
Sponsor: KK was supported by the National Science Center (Poland) post-doctoral internship grant on the basis of the decision No. DEC-2012/04/S/ST1/00093
Version: Published
DOI: 10.1685/journal.caim.534
URI: https://dspace.lboro.ac.uk/2134/18913
Publisher Link: http://dx.doi.org/10.1685/journal.caim.534
ISSN: 2038-0909
Appears in Collections:Published Articles (Maths)

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