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

TL;DR

This paper extends Strichartz inequalities to orthonormal functions linked with Dunkl Hermite and Dunkl Laplacian operators, establishing new bounds for solutions of Dunkl-related Schrödinger equations.

Contribution

It generalizes Strichartz inequalities to systems of orthonormal functions for Dunkl operators, connecting kernels of Dunkl Hermite and Dunkl Laplacian Schrödinger propagators.

Findings

Established relation between Schrödinger kernels of Dunkl Hermite and Dunkl Laplacian.

Derived Strichartz inequality for orthonormal functions with Dunkl Laplacian.

Extended known inequalities to a broader class of Dunkl-related 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.