Restriction theorem for the Fourier-Dunkl transform I: Cone surface

2022/12/04 by P Jitendra Kumar Senapati, Senapati, P Jitendra Kumar, Pradeep Boggarapu +5
Mathematics · #35P10 #43A32 #47B10 #Algebraic and Geometric Analysis #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Analysis and Transform Methods #Primary: 42A38 #Secondary: 42B35 #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2212.01886

openalex publication_date 2022/12/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this article, we define the Fourier-Dunkl transform, which generalizes the Fourier transform. We prove Strichartz's restriction theorem for the Fourier-Dunkl transform for a cone-hyper-surface and its generalisation to the family of orthonormal functions. As an application of this restriction theorem, we derive the Strichartz inequality associated with the square root of Dunkl Laplacian for the family of orthonormal functions.

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