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 lineWe 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. |

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University of Bialystok |

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