Levy processes Non-local Schrodinger operators Feynman-Kac semigroups Spectral properties Decay of eigenfunctions Lieb-Thirring inequality
Società Italiana di Matematica Applicata e Industriale (SIMAI)
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.
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.
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.
KK was supported by the National Science Center
(Poland) post-doctoral internship grant on the basis of the decision No.