International Journal of Mathematics and Mathematical Sciences
Volume 2010 (2010), Article ID 357050, 15 pages
doi:10.1155/2010/357050

An elementary construction on nonlinear coherent states associated to generalized Bargmann spaces

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.