- Series
- Analysis Seminar
- Time
- Wednesday, April 18, 2012 - 2:00pm for 1 hour (actually 50 minutes)
- Location
- Skiles 005
- Speaker
- Kelly Bickel – Washington University - St. Louis
- Organizer
- Brett Wick
It is well-known that every Schur function on the bidisk can be written as
a sum involving two positive semidefinite kernels. Such decompositions,
called Agler decompositions, have been used to answer interpolation
questions on the bidisk as well as to derive the transfer function
realization of Schur functions used in systems theory. The original
arguments for the existence of such Agler decompositions were
nonconstructive and the structure of these decompositions has remained
quite mysterious.
In this talk, we will discuss an elementary proof of the existence of
Agler decompositions on the bidisk, which is constructive for inner
functions. We will use this proof as a springboard to examine the
structure of such decompositions and properties of their associated
reproducing kernel Hilbert spaces.