Analysis Seminar

Hugo Woerdeman, Drexel University

“Rational Schur-Agler functions on polynomially-defined domains”

The converse question,“ is every rational inner function in the Schur-Agler class of the polydisk necessarily of the above form? led to questions regarding finite dimensional realizations of rational Schur-Agler functions, determinantal representations of stable polynomials, rational inner functions that are not Schur-Agler, and so forth. In this work we study these questions in Schur-Agler classes defined via a matrix-valued polynomial P, leading to domains of the type

j=1j 1 d p(z1,...,zd)

DP := {z = (z1,...,zd) ∈ Cd : P(z)∗P(z) < I}.

Aside from the polydisk this general setting also includes the unit ball Bd, and more gener- ally, Cartan’s classical domains. This talk is based on joint work with A. Grinshpan, D. S. Kaliuzhnyi-Verbovetskyi, and V. Vinnikov.