Analysis Seminar: "Composition Operators and Reproducing Kernel Hilbert Spaces"

Abstract: In this talk, I will talk about the boundedness of composition operators on the Hardy space H^2. On the unit disk, the Littlewood Subordination Principle shows that every composition operator is bounded on H^2(D). In 2007, M. Jury found another proof of this result using only reproducing kernels and de Branges-Rovnyak spaces. I would like to use this idea to study the composition operators on the Hardy space of the bidisk. It is known that not all composition operators are bounded and only some special functions induce bounded composition operators. I will suggest some ways to produce nontrivial bounded composition operators on H^2(D^2).

Organizer: John McCarthy