Beurling quotient modules on the polydisc

Abstract

Let H 2 (D n ) denote the Hardy space over the polydiscWe present two applications: first, we obtain a dilation theorem for Brehmer n-tuples of commuting contractions, and, second, we relate joint invariant subspaces with factorizations of inner functions. All results work equally well for general vector-valued Hardy spaces. Contents 1. Introduction 1 2. Proof of Theorem 1.1 4 3. Isometric dilations 9 4. Factorizations and invariant subspaces 10 References 14