论文标题
$（k，a）$广义的拉瓜运营商和dunkl操作员
Orthonormal Strichartz inequalities for the $(k, a)$-generalized Laguerre operator and Dunkl operator
论文作者
论文摘要
令$δ_{k，a} $和$δ_k$为$（k，a）$广义的laguerre操作员和dunkl laplacian运算符，分别在$ \ mathbb {r}^n $上。本文的目的是双重的。首先，我们证明了傅立叶$δ_{k，a} $变换的限制定理。接下来，作为限制问题的应用，我们建立了Schrödinger传播器$ e^{ - itδ_{k，a}} $与操作员$δ__{k，a} $相关的schrödinger繁殖者$ e^{ - itΔ__{k，a}} $的初始数据的估计。此外，使用经典的strichartz估计值，用于自由schrödingeropagator $ e^{ - itδ_{k，a}} $，用于初始数据的正交系统，以及半群的nemigroups $ e^{ - itδ__{k，a}} $ e^{ - itδ_{ \ frac {t} {a} \ | x \ |^{2-a}δ_{k}}，$我们证明了与dunkl operator $Δ_K$相关的初始数据的正常系统的估算值，$ \ nathbb {r}^n $。最后，我们为上述结果提供了一些应用。
Let $Δ_{k,a}$ and $Δ_k $ be the $(k,a)$-generalized Laguerre operator and the Dunkl Laplacian operator on $\mathbb{R}^n$, respectively. The aim of this article is twofold. First, we prove a restriction theorem for the Fourier-$Δ_{k,a}$ transform. Next, as an application of the restriction problem, we establish Strichartz estimates for orthonormal families of initial data for the Schrödinger propagator $e^{-i t Δ_{k, a}} $ associated with the operator $ Δ_{k, a}$. Further, using the classical Strichartz estimates for the free Schrödinger propagator $e^{-i t Δ_{k, a}} $ for orthonormal systems of initial data and the kernel relation between the semigroups $e^{-i t Δ_{k, a}}$ and $e^{i \frac{t}{a}\|x\|^{2-a} Δ_{k}},$ we prove Strichartz estimates for orthonormal systems of initial data associated with the Dunkl operator $ Δ_k $ on $\mathbb{R}^n$. Finally, we present some applications to our aforementioned results.
