Event № 177
This talk is devoted to semigroups of composition operators and semigroups of holomorphic mappings on the right half-plane. We establish conditions under which these semigroups can be extended in their parameter to a sector given a priori. We show that the size of this sector can be controlled by the image properties of the infinitesimal generator, or, equivalently, by the geometry of the so-called associated planar domain. We also give a complete characterization of all composition operators acting on the Hardy space $H^p$ on the right half-plane. This is joint work with Fiana Jacobzon.