Wednesday, 20 November, 2013
SPEAKER: Prof. Kelly Bickel, Georgia Tech
TITLE: Agler Kernels on Bidisk
ABSTRACT: Representation theorems for (bounded) holomorphic functions on the unit disk, such as inner-outer factorizations, rarely generalize to the two variable setting. In this talk, we discuss a successful method for representing bounded functions on the bidisk, which was pioneered by J. Agler and has been used to generalize many one variable results to two variables. This method has close ties to systems theory specifically linear input/state/output systems, and operator theory via von Neumann's Inequality.
The basic idea is to decompose a bounded function into a sum of two positive kernels, called Agler kernels. The original proof of the existence of such decompositions was nonconstructive and we will discuss a constructive method for obtaining Agler kernels. The construction implies additional properties about the representation formula and associated Hilbert spaces. Time permitting, we will discuss the implications for bounded holomorphic functions on the tridisk. This talk is based on joint work with Greg Knese.