XXXVIII Workshop on Geometric Methods in Physics 30.06-6.07.2019 VIII School on Geometry and Physics 24-28.06.2019
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# Zouhair Mouayn

## Nonlinear coherent states associated with a measure on the positive real half line

We construct a class of generalized nonlinear coherent states by means of a newly obtained class of 2D complex orthogonal polynomials. The associated coherent states transform is discussed. A polynomials realization of the basis of the quantum states Hilbert space is also given. Here, the entire structure owes its existence to a certain measure on the positive real half line, of finite total mass, together with all its moments. We illustrate this construction with the example of the measure $r^\beta e^{-r}dr$, which leads to a new generalization of the true-polyanalytic Bargmann transform.

KEYWORDS: Nonlinear coherent states; 2D complex orthogonal polynomials; Bargmann-type transform, positive measure on $\mathbb{R}_+$.

AMS CLASSIFICATION: 33C45; 81R30; 35A22.

 Event sponsored by: University of Bialystok

Webpage by: Tomasz Golinski