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Doubly commuting submodules of the Hardy module over polydiscs
classification
🧮 math.FA
math.CVmath.OA
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theoremapplicationbeurlingcommutingcompletionconditionsdoublyestablish
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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 $H^\infty(\mathbb{D}^n)$.
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