4 papers
Stable polynomials and bounded rational functions in the unit ball
Greg Knese, James Eldred Pascoe, Alan Sola
We study polynomials with no zeros on the unit ball in complex Euclidean space with a view toward characterizing when a rational function is bounded on the ball. We give a complete…
The Schur-Agler class in infinitely many variables
Greg Knese
We define the Schur-Agler class in infinite variables to consist of functions whose restrictions to finite dimensional polydisks belong to the Schur-Agler class. We show that a nat…
Testing von Neumann inequalities with nilpotent matrices
Greg Knese
We give an elementary proof of the folklore result that the Agler norm of a function is determined by its norm on commuting tuples of nilpotent matrices. The proof is variation on…
Hadamard multipliers of the Agler class
Greg Knese
We prove several results about functions which preserve the Schur-Agler class under Hadamard or coefficient-wise product. First, functions which preserve the Schur class necessaril…