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
Bangalore.

 

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
       Pick-interpolation problem”

 

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.