1Indian Statistical Institute Statistics and Mathematics Unit 8th Mile, Mysore Road Bangalore, 560059, India 2Mathematics Department London School of Economics Houghton Street London WC2A 2AE, U.K. 3School 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
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 $H^\infty (\mathbb {D}^n)$.
Keywords:
note establish vector valued version beurlings theorem lax halmos theorem polydisc application main result provide necessary sufficient conditions weak completion problem infty mathbb
Affiliations des auteurs :
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
