Doubly commuting submodules of the Hardy module over polydiscs
Sarkar, J., Sasane, A.
& Wick, B. D.
(2013).
Doubly commuting submodules of the Hardy module over polydiscs.
Studia Mathematica,
217(2), 179-192.
https://doi.org/10.4064/sm217-2-5
& Wick, B. D.
(2013).
Doubly commuting submodules of the Hardy module over polydiscs.
Studia Mathematica,
217(2), 179-192.
https://doi.org/10.4064/sm217-2-5
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 ∞ (D n ) .