We construct a class of generalized nonlinear coherent states by means of a newly obtained class of 2D complex orthogonal polynomials. The associated Bargmann-type transform is discussed. A polynomials realization of the basis of the quantum states Hilbert space is also obtained. 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 method with the measure \(r^\beta e^{-r}dr\), where \(\beta \) is a non-negative constant, which leads to a new generalization of the true-polyanalytic Bargmann transform.

中文翻译：

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与正实半线上的测度相关的非线性相干态

我们借助于新获得的一类二维复正交多项式构造一类广义非线性相干态。讨论了相关的Bargmann型变换。还获得了量子态希尔伯特空间基础的多项式实现。在这里，整个结构的存在归因于存在于总质量有限的正实半线上的确定的度量，以及所有的矩。我们用量度\（r ^ \ beta e ^ {-r} dr \）来说明这种方法，其中\（\ beta \）是非负常数，这导致真多解析Bargmann变换的新概括。