论文标题
当q^{ - 1}> 1时，真流式巴尔格曼的Q变形会转换
A q deformation of true-polyanalytic Bargmann transforms when q^{-1}> 1
论文作者
论文摘要
我们将连续的$ q^{ - 1} $ - Hermite ASKEY多项式与Ismail和Zhang引入的新$ 2D $正交多项式作为$ Q $ -Analogs，用于复杂的HERMITE多项式，以构建一套新的相干状态，这些状态取决于非智力integer integer integer integer参数。在与$ m = 0 $相对应的分析案例中，我们以$ q'= q'= q'= q^{ - 1}> 1 $恢复了已知结果 过程。
We combine continuous $q^{-1}$-Hermite Askey polynomials with new $2D$ orthogonal polynomials introduced by Ismail and Zhang as $q$-analogs for complex Hermite polynomials to construct a new set of coherent states depending on a nonnegative integer parameter $m$. In the analytic case corresponding to $m=0$, we recover a known result on the Ar\"ık-Coon oscillator for $q'=q^{-1}>1$. Our construction leads to a new $q$-deformation of the $m$-true-polyanalytic Bargmann transform on the complex plane. The obtained result may be used to introduce a $q$-deformed Ginibre-type point process.
