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

TL;DR

This paper proves restriction theorems for the Fourier-Laguerre transform and establishes Strichartz estimates for the Schrödinger propagator associated with the Laguerre operator, involving orthonormal functions, on positive real space.

Contribution

It introduces new restriction theorems and Strichartz estimates for the Laguerre operator with orthonormal functions, expanding harmonic analysis tools in this context.

Findings

Restriction theorems for Fourier-Laguerre transform established.

Strichartz estimates for Schrödinger propagator proved.

Results applicable to systems of orthonormal functions on a7^n.

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.