## State space methods in operator and function theory

#### Location

Cupples I Room 113

#### Start Date

7-19-2016 5:30 PM

#### End Date

19-7-2016 5:50 PM

#### Description

There are three new things in this talk about the open symmetrized bidisk $\mathbb G = \{ (z_1+z_2, z_1z_2) : |z_1|, |z_2| < 1\}$. \begin{enumerate} \item The Realization Theorem: A realization formula is demonstrated for every $f$ in the norm unit ball of $H^\infty(\mathbb G)$. \item The Interpolation Theorem: Nevanlinna-Pick interpolation theorem is proved for data from the symmetrized bidisk and a specific formula is obtained for the interpolating function. \item The Extension Theorem: A characterization is obtained of those subsets $V$ of the open symmetrized bidisk $\mathbb G$ that have the property that every function $f$ holomorphic in a neighbourhood of $V$ and bounded on $V$ has an $H^\infty$-norm preserving extension to the whole of $\mathbb G$. \end{enumerate}

#### Share

COinS

Jul 19th, 5:30 PM Jul 19th, 5:50 PM

Holomorphic functions on the symmetrized bidisk - realization, interpolation and extension

Cupples I Room 113

There are three new things in this talk about the open symmetrized bidisk $\mathbb G = \{ (z_1+z_2, z_1z_2) : |z_1|, |z_2| < 1\}$. \begin{enumerate} \item The Realization Theorem: A realization formula is demonstrated for every $f$ in the norm unit ball of $H^\infty(\mathbb G)$. \item The Interpolation Theorem: Nevanlinna-Pick interpolation theorem is proved for data from the symmetrized bidisk and a specific formula is obtained for the interpolating function. \item The Extension Theorem: A characterization is obtained of those subsets $V$ of the open symmetrized bidisk $\mathbb G$ that have the property that every function $f$ holomorphic in a neighbourhood of $V$ and bounded on $V$ has an $H^\infty$-norm preserving extension to the whole of $\mathbb G$. \end{enumerate}