International Journal of Mathematics and Mathematical Sciences
Volume 2010 (2010), Article ID 357050, 15 pages
Research Article

An Elementary Construction on Nonlinear Coherent States Associated to Generalized Bargmann Spaces

1Equipe d'Analyse spectrale, UMR-CNRS n : 6134, Université de Corse, Quartier Grossetti, 20 250 Corté, France
2Le Prador, 129 rue du Commandant Rolland, 13008 Marseille, France

Received 27 July 2009; Revised 28 December 2009; Accepted 11 February 2010

Academic Editor: Ricardo Estrada

Copyright © 2010 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.


Consider the space L2(,dμ(z)), where dμ(z)=e|z|2dzdz¯ is the Gaussian measure, and its generalized Bargmann subspaces Em which are the null kernels of the operator Δ=-2/zz¯+z¯(/z¯)-mI;   m=0,1,. In this work, we present an other construction of Em following the Hermite functions which allows us to define a family of generalized Bargmann transform Bm which maps isometrically Em into L2(). The generalized coherent states zm associated to Em are constructed and some properties of them are given.