Geodesic
Doubly commuting submodules of the Hardy module over polydiscs
Jaydeb Sarkar 1   ; Amol Sasane 2   ; Brett D. Wick 3
1 Indian Statistical Institute Statistics and Mathematics Unit 8th Mile, Mysore Road Bangalore, 560059, India
2 Mathematics Department London School of Economics Houghton Street London WC2A 2AE, U.K.
3 School of Mathematics Georgia Institute of Technology 686 Cherry Street Atlanta, GA 30332-0160, U.S.A.
Studia Mathematica, Tome 217 (2013) no. 2, pp. 179-192 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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 “weak” completion problem in $H^\infty (\mathbb {D}^n)$.
DOI : 10.4064/sm217-2-5
Keywords: note establish vector valued version beurlings theorem lax halmos theorem polydisc application main result provide necessary sufficient conditions weak completion problem infty mathbb

Jaydeb Sarkar  1   ; Amol Sasane  2   ; Brett D. Wick  3

1 Indian Statistical Institute Statistics and Mathematics Unit 8th Mile, Mysore Road Bangalore, 560059, India
2 Mathematics Department London School of Economics Houghton Street London WC2A 2AE, U.K.
3 School of Mathematics Georgia Institute of Technology 686 Cherry Street Atlanta, GA 30332-0160, U.S.A. 
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Jaydeb Sarkar; Amol Sasane; Brett D. Wick. Doubly commuting submodules of the Hardy module over polydiscs. Studia Mathematica, Tome 217 (2013) no. 2, pp. 179-192. doi: 10.4064/sm217-2-5

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