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.

Abstract

Consider the space L2(ℂ,dμ(z)), where dμ(z)=e−|z|2dz∧dz¯ is the Gaussian measure, and its generalized Bargmann subspaces Em which are the null kernels of the operator Δ=-∂2/∂z∂z¯+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(ℝ). The generalized coherent states ∣z〉m associated to Em are constructed and some properties of them are given.