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

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})} .