论文标题
傅里叶丁克变换的限制定理II：抛物面，球体和倍或倍或倍虫表面
Restriction theorem for Fourier-Dunkl transform II: Paraboloid, sphere, and hyperboloid surfaces
论文作者
论文摘要
这是论文“傅里叶丁克变换的限制定理I：锥形表面，J。Pseudo-differ。plop。Appl。Appl。14（1），第5号论文（2023）”，作者在其中介绍并研究了$ \ \ Mathbb {r}^n}^{n}^{n}^{n}^{n} \ times \ mathb} $} $} $}本文的主要新颖性是，我们在这里证明了Strichartz对某些表面的傅立叶丁克变换的限制定理，即，抛物面，球体和倍或倍或倍或倍或倍曲底，及其对正常函数家族的概括。最后，作为这些限制定理的应用，我们在Dunkl Laplacian和Klein-Gordon操作员的情况下，建立了与Schrödinger的繁殖者相关的初始数据的正顺序家族的版本。
This is a continuation of the paper "Restriction theorem for Fourier-Dunkl transform I: Cone surface, J. Pseudo-Differ. Oper. Appl. 14(1), Paper No. 5 (2023)", where the authors introduced and studied the Fourier-Dunkl transform on $\mathbb{R}^{n}\times\mathbb{R}^{d}$. The main novelty of this paper is that we here prove Strichartz's restriction theorem for the Fourier-Dunkl transform for certain surfaces, namely, paraboloid, sphere, and hyperboloid and its generalisation to the family of orthonormal functions. Finally, as an application of these restriction theorems, we establish versions of Strichartz estimates for orthonormal families of initial data associated with Schrödinger's propagator in the case of the Dunkl Laplacian and Klein-Gordon operator.
