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

In this paper, we prove restriction theorems for the Fourier-Laguerre transform and establish Strichartz estimates for the Schrödinger propagator $e^{-itL_α}$ for the Laguerre operator $L_α=-Δ-\sum_{j=1}^{n}(\dfrac{2α_j+1}{x_j}\dfrac{\partial}{\partial x_j})+\dfrac{|x|^2}{4}$, $α=(α_1,α_2,\cdots,α_n)\in{(-\frac{1}{2},\infty)^n}$ on $\mathbb{R}_+^n$ involving systems of orthonormal functions.

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