M. Savov (Reading)

Some spectral problems associated to positive self-similar Markov processes

Abstract: In this talk we discuss the discrete spectrum of stationary semi-groups related to positive self-similar Markov processes via intertwining with a single underlying Bessel process. When the spectrum is purely discrete we discuss some spectral expansions and why they fail on the Hilbert space H generated by the stationary measures of the semi-groups. It turns out that spectral expansion is indeed possible on a large subset of H which suffices for the description of the semi-groups but fails on the whole space. We discuss also the reasons for this. This study is carried jointly with Pierre Patie (Cornell, US).