Une $q$-d\'eformation de la transformation de Bargmann polyanalytique

TL;DR

This paper introduces a $q$-analog of the polyanalytic Bargmann transform, extending classical analysis tools into the quantum calculus framework on the complex plane.

Contribution

It presents the first construction of a $q$-deformed polyanalytic Bargmann transform, bridging classical and quantum analysis.

Findings

Defined the $q$-analog of the polyanalytic Bargmann transform

Established properties and potential applications of the transform

Extended classical analysis into the quantum calculus setting

Abstract

We introduce a $q$-analog of the polyanalytic Bargmann transform on $\mathbb{C}$.