Restriction theorems and Strichartz inequalities for the Laguerre operator involving orthonormal functions

Abstract

In this paper, we prove restriction theorems for the Fourier-Laguerre transform and establish Strichartz estimates for the Schr\"{o}dinger propagator $e^{-itL_\alpha}$ for the Laguerre operator $L_\alpha=-\Delta-\sum_{j=1}^{n}(\dfrac{2\alpha_j+1}{x_j}\dfrac{\partial}{\partial x_j})+\dfrac{|x|^2}{4}$, $\alpha=(\alpha_1,\alpha_2,\cdots,\alpha_n)\in{(-\frac{1}{2},\infty)^n}$ on $\mathbb{R}_+^n$ involving systems of orthonormal functions.