Local theory of stable polynomials and bounded rational functions in two variables

Speaker: Alan Sola (Stockholm University)

Abstract:

We will discuss boundary behavior of bounded rational functions in the bidisk from several perspectives, including existence of non-tangential limits and higher non-tangential regularity. The results we obtain rely heavily on local descriptions of stable polynomials, which lead to a conjecture (since resolved by J. Kollar) regarding the characterization of bounded rational functions with a given stable denominator.

This reports on joint work with K. Bickel, G. Knese, and J.E. Pascoe.