Analysis Seminar: "Local theory of stable polynomials and the admissible numerator problem"

Abstract: Given rational function on the bidisk, when is it bounded?  Given a fixed denominator p, can we describe all numerators such that q/p is bounded?  We shall give some answers to these basic questions by pursuing a very detailed local structure theorem for stable polynomials (polynomials with no zeros on the bidisk) near a boundary zero.  We can give a complete characterization of the admissible numerators for certain “tame” boundary singularities (smooth points, double points, ordinary multiple points) and we have a tantalizing conjecture for all cases. This is joint work with Bickel, Pascoe, Sola.

Host: John McCarthy