An Elementary Construction on Nonlinear Coherent States Associated to Generalized Bargmann Spaces - Abdelkader Intissar (International Journal of Mathematics and Mathematical Sciences)
Consider the space 𝐿2(ℂ,𝑑𝜇(𝑧)), where 𝑑𝜇(𝑧)=𝑒−|𝑧|2⋀𝑑𝑑𝑧𝑧 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.