Dunkl-type Segal–Bargmann transform and its applications to some partial differential equations

Pub Date : 2024-06-25 DOI:10.1515/gmj-2024-2031

Fethi Soltani, Meriem Nenni

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Abstract

In this paper, we give some applications of the Dunkl-type Segal–Bargmann transform ℬ α

{\mathscr{B}_{\alpha}}

in the field of partial differential equations, such as the time-dependent Dunkl–Dirac Laplacian equation and the time-dependent Dunkl–Schrödinger equation. The resolution of these types of problems is based on the techniques of the transmutation operators on the Dunkl-type Fock space ℱ α ⁢ ( ℂ d )

{\mathscr{F}_{\alpha}(\mathbb{C}^{d})}

.

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Dunkl 型 Segal-Bargmann 变换及其在某些偏微分方程中的应用

本文给出了邓克尔型西格尔-巴格曼变换ℬ α {mathscr{B}_{\alpha}} 在偏微分方程领域的一些应用，例如时变邓克尔-狄拉克拉普拉斯方程和时变邓克尔-薛定谔方程。这类问题的解决基于邓克尔型福克空间 ℱ α ( ℂ d ) {mathscr{F}_{\alpha}(\mathbb{C}^{d})} 上的嬗变算子技术。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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