Spectral properties of a class of non-local operators via a stochastic representation

Speaker: Jozsef Lorinczi (Loughborough University)

Fractional Schrödinger and jump-diffusion operators provide useful tools in modelling relativistic quantum and anomalous kinetic phenomena. Driven by such applications I will formulate some problems involving spectral and analytic properties of evolution semigroups generated by these operators. By using a Feynman-Kac representation of the semigroups I will explain how to obtain the desired spectral information by exploiting the properties of the stochastic processes the given operators give rise to.

Part of the Stochastic Analysis Seminar Series