Comptes Rendus
Functional analysis
Rudin's submodules of H2(D2)
Comptes Rendus. Mathématique, Volume 353 (2015) no. 1, pp. 51-55.

Let {αn}n0 be a sequence of scalars in the open unit disc of C, and let {ln}n0 be a sequence of natural numbers satisfying n=0(1ln|αn|)<. Then the joint (Mz1,Mz2) invariant subspace

is called a Rudin submodule. In this paper, we analyze the class of Rudin submodules and prove that
In particular, this answers a question earlier raised by Douglas and Yang (2000) [4].

Soit {αn}n0 une suite de scalaires du disque unité ouvert de C, et soit {ln}n0 une suite de nombres naturels vérifiant n=0(1ln|αn|)<. Alors le sous-espace invariant (Mz1,Mz2)

est appelé sous-module de Rudin. Dans cette Note, on analyse la classe des sous-modules de Rudin et on démontre que
En particulier, ce résultat répond à une question posée précédemment par Douglas et Yang (2000) [4].

Published online:
DOI: 10.1016/j.crma.2014.10.005

B. Krishna Das 1; Jaydeb Sarkar 1

1 Indian Statistical Institute, Statistics and Mathematics Unit, 8th Mile, Mysore Road, Bangalore, 560059, India
     author = {B. Krishna Das and Jaydeb Sarkar},
     title = {Rudin's submodules of $ {H}^{2}({\mathbb{D}}^{2})$},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {51--55},
     publisher = {Elsevier},
     volume = {353},
     number = {1},
     year = {2015},
     doi = {10.1016/j.crma.2014.10.005},
     language = {en},
AU  - B. Krishna Das
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JO  - Comptes Rendus. Mathématique
PY  - 2015
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EP  - 55
VL  - 353
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PB  - Elsevier
DO  - 10.1016/j.crma.2014.10.005
LA  - en
ID  - CRMATH_2015__353_1_51_0
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%0 Journal Article
%A B. Krishna Das
%A Jaydeb Sarkar
%T Rudin's submodules of $ {H}^{2}({\mathbb{D}}^{2})$
%J Comptes Rendus. Mathématique
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B. Krishna Das; Jaydeb Sarkar. Rudin's submodules of $ {H}^{2}({\mathbb{D}}^{2})$. Comptes Rendus. Mathématique, Volume 353 (2015) no. 1, pp. 51-55. doi : 10.1016/j.crma.2014.10.005.

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