Bergman inner functions and m-hypercontractions

摘要

We characterize operator-valued Bergman inner functions on the unit ball as functions admitting a suitable transfer function realization. Thus we extend corresponding one variable results of Olofsson from the case of the unit disc to the unit ball. At the same time we associate with each m-hypercontraction T is an element of L(H)(n) a canonical Bergman inner function WT and indicate a possible definition of a characteristic function theta(T) for T. (C) 2017 Elsevier Inc. All rights reserved.