Analysis Seminar: "Local theory of stable polynomials and the admissible numerator problem"
Speaker: Greg Knese, Washington University in Saint Louis
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