Rudin's submodules of

@@113053@@EM|consulte.

Article

Article Outline

Access to the text (HTML)

Access to the PDF text

Recommend this article

Save as favorites

Advertising

Access to the full text of this article requires a subscription.

If you are a subscriber, please sign in 'My Account' at the top right of the screen.

If you want to subscribe to this journal, see our rates

You can purchase this item in Pay Per View : 30,00 € Taxes included to order

Pages Iconography Videos Other

5 0 0 0

Comptes Rendus Mathématique
Volume 353, n° 1
pages 51-55 (janvier 2015)

Doi : 10.1016/j.crma.2014.10.005

Received : 6 May 2014 ; accepted : 10 October 2014

Rudin's submodules of

Sous-modules de Rudin de

B. Krishna Das , Jaydeb Sarkar
Indian Statistical Institute, Statistics and Mathematics Unit, 8th Mile, Mysore Road, Bangalore, 560059, India


	Abstract

Let be a sequence of scalars in the open unit disc of , and let be a sequence of natural numbers satisfying . Then the joint invariant subspace
SΦ=⋁n=0∞(z1n∏k=n∞(−α¯k|αk|z2−αk1−α¯kz2)lkH2(D2)), is called a Rudin submodule. In this paper, we analyze the class of Rudin submodules and prove thatdim(SΦ⊖(z1SΦ+z2SΦ))=1+#{n≥0:αn=0}<∞. In particular, this answers a question earlier raised by Douglas and Yang (2000) [[4]].

The full text of this article is available in PDF format.


	Résumé

Soit une suite de scalaires du disque unité ouvert de , et soit une suite de nombres naturels vérifiant . Alors le sous-espace invariant
SΦ=⋁n=0∞(z1n∏k=n∞(−αk¯|αk|z2−αk1−α¯kz2)lkH2(D2)), est appelé sous-module de Rudin. Dans cette Note, on analyse la classe des sous-modules de Rudin et on démontre quedim(SΦ⊖(z1SΦ+z2SΦ))=1+#{n≥0:αn=0}<∞. En particulier, ce résultat répond à une question posée précédemment par Douglas et Yang (2000) [[4]].

The full text of this article is available in PDF format.

Outline

Top of the page - Article Outline

EM-CONSULTE.COM is registrered at the CNIL, déclaration n° 1286925.
As per the Law relating to information storage and personal integrity, you have the right to oppose (art 26 of that law), access (art 34 of that law) and rectify (art 36 of that law) your personal data. You may thus request that your data, should it be inaccurate, incomplete, unclear, outdated, not be used or stored, be corrected, clarified, updated or deleted.
Personal information regarding our website's visitors, including their identity, is confidential.
The owners of this website hereby guarantee to respect the legal confidentiality conditions, applicable in France, and not to disclose this data to third parties.

Article Outline

You can move this window by clicking on the headline