Department of Mathematics
Indian Institute of Science
Bangalore 560 012
SEMINAR
Speaker |
: |
Dr. Gautam Bharali |
Affiliation | : |
IISc |
Subject Area |
: |
Mathematics
|
Venue |
: |
Lecture Hall - I, Dept of Mathematics
|
Time |
: |
4.00 pm
|
Date |
: |
November 16,2007 (Friday) |
Title |
: |
Spectral Pick interpolation from a complex-geometric viewpoint |
Abstract | : |
The spectral Pick-interpolation problem, i.e. to determine when there exists a holomorphic map from the unit disc to the class of complex matrices of spectral radius less than one that interpolates prescribed data, has a complicated solution using operator-theory and control-theory methods. The difficulty in implementing this solution motivated a new approach pioneered by Agler and Young. Their methods led to a checkable necessary condition for Pick interpolation. But, from a complex-geometric viewpoint, it was unclear why the latter condition should be sufficient. In this talk, we will demonstrate that this condition is not sufficient. We will also present an inequality -- largely linear-algebraic in flavour -- that provides a necessary condition for matricial data for which the Agler-Young-type test provides no conclusions. |