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
Das, B. Krishna 1; Sarkar, Jaydeb 1

1 Indian Statistical Institute, Statistics and Mathematics Unit, 8th Mile, Mysore Road, Bangalore, 560059, India
     author = {Das, B. Krishna and Sarkar, Jaydeb},
     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},
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Das, B. Krishna; Sarkar, Jaydeb. 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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