Title:
Spectral Properties of a Class of Non-Local Operators by Stochastic 
Methods

Abstract:

Fractional Schr?dinger 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
Bernstein functions of the Laplacian, including these operators as
special cases. By using a combination of functional integration,
potential theory and Wiener-Hopf methods, I will present results on
asymptotic properties of the spectrum and eigenfunctions of the 
non-local operators involved.