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arXiv · 2212.11052

Restriction theorem for Fourier-Dunkl transform II: Paraboloid, sphere, and hyperboloid surfaces

P Jitendra Kumar Senapati·Pradeep Boggarapu·Shyam Swarup Mondal·Hatem Mejjaoli
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Abstract

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.

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P Jitendra Kumar Senapati, Pradeep Boggarapu, Shyam Swarup Mondal, Hatem Mejjaoli. 2022-12-21. Restriction theorem for Fourier-Dunkl transform II: Paraboloid, sphere, and hyperboloid surfaces. https://arxiv.org/abs/2212.11052

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