Doubly commuting submodules of the Hardy module over polydiscs (1302.5312v3)

Published 21 Feb 2013 in math.FA, math.CV, and math.OA

Abstract: In this note we establish a vector-valued version of Beurling's Theorem (the Lax-Halmos Theorem) for the polydisc. As an application of the main result, we provide necessary and sufficient conditions for the completion problem in $H^{\infty(\mathbb{D}^n)$.}