Doubly commuting submodules of the Hardy module over polydiscs
Volume 217 / 2013
Studia Mathematica 217 (2013), 179-192
MSC: Primary 46J15; Secondary 47A15, 30H05, 47A56.
DOI: 10.4064/sm217-2-5
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 “weak” completion problem in $H^\infty (\mathbb {D}^n)$.
