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

Consider the space L2 C, dμ z , where dμ z e−|z| 2 dz ∧ 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.