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 Schrödinger propagator $e^{-it{L}_{\hat{I}}\pm }$ for the Laguerre operator $L_{\hat{I}}\pm =-\hat{I}”-{\sum }_{j=1}^n(\frac{2\hat{I}{\pm }_j+1}{x_j}\frac{\partial }{\partial x_j})+\frac{|x{|}^2}{4}$, $\hat{I}\pm =(\hat{I}{\pm }_1,\hat{I}{\pm }_2,\cdots ,\hat{I}{\pm }_n)\in (-\frac{1}{2},\infty {)}^n$ on ${\mathbb{R}}_{+}^n$ involving systems of orthonormal functions.