Department of Mathematics
Indian Institute of Science
Bangalore 560 012
GOLDEN JUBILEE YEAR 2005 - 2006
SEMINAR.....
Speaker |
: |
Dr. Gautam Bharali
|
Affiliation |
: |
Indian Institute of Science |
Subject Area |
: |
Mathematics
|
Venue |
: |
Lecture Hall III, Dept of Mathematics
|
Time |
: |
4.00 pm
|
Date |
: |
Friday, 10th February,2006
|
Event Title1 |
: |
"Recent progress on the spectral
|
Abstract |
Given N distinct points z_1,...,z_N in the
unit disc, and m-by-m complex matrices W_1,...,W_N whose spectral radii are
less than 1, the spectral Pick-interpolation problem is to find a necessary
and sufficient condition on the given data so that there exists a
(matrix-valued) complex-analytic function on the unit disc that interpolates
the given data and takes values in the class of matrices having spectral
radii less than 1. This twisted version of the classical Pick problem is
motivated by a problem in control theory. We shall survey some recent
progress on this problem - most of which comes from operator theory - and
look at the obstructions to the operator-theoretic approach resulting from
the fact that the spectral radius is not a norm. Lastly, we shall examine
some recent ideas from several complex variables on how the aforementioned
obstructions might be circumvented. |