Contact Info
Pure MathematicsUniversity of Waterloo
200 University Avenue West
Waterloo, Ontario, Canada
N2L 3G1
Departmental office: MC 5304
Phone: 519 888 4567 x33484
Fax: 519 725 0160
Email: puremath@uwaterloo.ca
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.
Departmental office: MC 5304
Phone: 519 888 4567 x33484
Fax: 519 725 0160
Email: puremath@uwaterloo.ca