A Caratheodory theorem for the bidisk via Hilbert space methods

Jim Agler, John E. McCarthy, Nicholas J. Young

If $\ph$ is an analytic function bounded by 1 on the bidisk $\D^2$ and $τ\in\tb$ is a point at which $\ph$ has an angular gradient $\nabla\ph(τ)$ then $\nabla\ph(\la) \to \nabla\ph…