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Advances in Mathematical Physics
Volume 2011, Article ID 471314, 11 pages
http://dx.doi.org/10.1155/2011/471314
Research Article

On a Chaotic Weighted Shift 𝑧 𝑝 𝑑 𝑝 + 𝟏 / 𝑑 𝑧 𝑝 + 𝟏 of Order 𝑝 in Bargmann Space

1Equipe d'Analyse Spectrale, Université de Corse, UMR-CNRS No. 6134, Quartier Grossetti, 20 250 Corté, France
2Le Prador, 129 rue du Commandant Rolland, 13008 Marseille, France

Received 19 March 2011; Accepted 9 May 2011

Academic Editor: B. G. Konopelchenko

Copyright © 2011 Abdelkader Intissar. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

This paper is devoted to the study of the chaotic properties of some specific backward shift unbounded operators 𝐻 𝑝 = 𝐴 𝑝 𝐴 𝑃 + 1 ; 𝑝 = 0 , 1 , realized as differential operators in Bargmann space, where 𝐴 and 𝐴 are the standard Bose annihilation and creation operators such that [ 𝐴 , 𝐴 ] = 𝐼 .