Caltech/UCLA Joint Analysis Seminar

SEMINAR WILL BE HELD AT UCLA MS 6627

Let J be the set of inner functions whose derivatives lie in Nevanlinna class. In this talk, we show that the natural map F -> Inn(F') : J/(Aut D) -> Inn/S^1 is injective. We also show that the image is closed under multiplication and taking divisors; however, the question of surjectivity remains open. Our proof is based on extending the work of D. Kraus and O. Roth on maximal Blaschke products to allow for singular factors. This partially answers a question raised by K. Dyakonov.