Pure Math colloquium

Vern Paulsen, University of Houston

“Operator Algebras and Nevanlinna-Pick Interpolation”

Given points z1,...,zn and w1,...,wn in the unit disk D, a theorem of Pick gives necessary and sufficient conditions for there to exist an analytic function f : D → D that interpolates these points, i.e., such that f(zi) = wi for all i. Independently, Nevanlinna proved a factorization theorem for analytic functions from the disk to the disk, which is equivalent to Picks theorem. Since then, math- ematicians have sought analogous theorems for the analytic functions from other complex domains to the disk. This program is largely unsuccessful—answers are not even known for polydisks and balls. But in the mid 1980s, J. Agler obtained some generalizations of these results, provided that one was willing to replace “complex variables” by “operator variables’. In this talk we will survey these ideas and then present a generalization of Agler’s results that we have obtained with M. Mittal using the theory of abstract operator algebras.

Please note the room is QNC 2502.

Refreshments will be served in MC 5046 at 3:30 p.m. Everyone is welcome to attend.