Strichartz inequality for orthonormal functions associated with Dunkl Laplacian and Hermite-Schr\"{o}dinger operators

Abstract

Strichartz inequality for the solutions of free Schr\"odinger equation associated with Dunkl Hermite operator $H_\kappa$ is generalized to any system of orthonormal functions with initial data. A relation between the kernels of Schr\"odinger propagators ($e^{-it H_\kappa}$ and $e^{it\Delta_\kappa}$) associated with the Dunkl Hermite and Dunkl Laplacian operators is established using which corresponding Schtrichartz inequality for orthonormal functions associated with Dunkl Laplacian is obtained.