Title: Spectral Pick interpolation from a complex-geometric viewpoint
Speaker: Dr. Gautam Bharali
Date: 16 November 2007
Time: 4.00 p.m.
Venue: Lecture Hall - I, Dept. of Mathematics
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.