Analysis Seminar : Austin Anderson (Kapi’olani Community College)

October 10, 2017 @ 3:30 pm – 4:30 pm
Keller 402

Title: Composition semigroups on spaces of analytic functions

Abstract : A semigroup {phi_t}_{t geq 0} of analytic self-maps of the disk satisifies phi_t circ phi_s = phi_{t+s}, and induces a semigroup of composition operators. We study the maximal space of strong continuity when the composition operators act on spaces of analytic functions, particularly H^{infty}, BMOA, and the Bloch space. We show that not every composition semigroup is strongly continuous on BMOA, answering a question that had remained open in the literature since at least 1998. This is joint work with Wayne Smith and Mirjana Jovovic.