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).