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Ground state properties of a class non-local Schrödinger operators

Jozsef Lorinczi
(Loughborough University)
Onsdag, 28 maj, 2014, at 15:15-16:15, in Aud. D4 (1531-219)
A non-local Schrödinger operator is the sum of a pseudo-differential operator (for instance, a fractional Laplacian) and a multiplication operator called potential. In this talk I will present recent results on spectral and analytic properties of such operators and their evolution semigroups by using stochastic methods. First I discuss some cases in which closed formulae can be obtained. Then I will explain the relationship of these operators and random processes with jump discontinuities (Lévy-type processes). Using these processes I will discuss how should the potential be chosen so that the Feynman-Kac semigroup of the perturbed process is intrinsically ultracontractive. I will also explain spatial decay properties of the eigenfunctions, and if time allows, will mention further aspects such as Lieb-Thirring bounds or fluctuations of these processes.
Kontaktperson: Jacob Schach Møller