Stephan
Garcia
Pomona College
Monday, April 21
Davidson Lecture
Hall at Claremont McKenna, 3:00 PM
Title: Inner Matrix Functions and Darlington
Synthesis
Abstract:
An inner function is a bounded analytic
function on the unit disk whose boundary values are almost everywhere
of unit modulus (we'll briefly explain why you should care). The
explicit structure of scalar inner functions is classical and
well-known (we'll do a brief recap to get everyone up to speed).
In fact, it's safe to say that scalar inner functions are quite well
understood. On the other hand, the explicit structure of
matrix-valued inner functions is considerably more difficult. A
careful analysis of the 2x2 case reveals a hidden quaternionic
structure. We are also able to give an explicit solution to a
certain matrix extension problem which originated in electrical
engineering.