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

2022/12/21 by P Jitendra Kumar Senapati, Senapati, P Jitendra Kumar, Pradeep Boggarapu +5 · 3 citations
Mathematics · #43A32 #47B10 #Analysis of PDEs (math.AP) #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Fourier analysis #Fourier inversion theorem #Fourier transform #Fractional Fourier transform #Geometry #Hyperboloid #Laplace operator #Mathematical Analysis and Transform Methods #Mathematical analysis #Mathematics #Orthonormal basis #Paraboloid #Physics #Primary: 42A38 #Pure mathematics #Quantum mechanics #Secondary: 42B35 #Spectral Theory in Mathematical Physics #Surface (topology)

paper · pdf · doi:10.48550/arxiv.2212.11052

openalex publication_date 2022/12/21 · openalex created_date 2023/01/04 · openalex updated_date 2026/08/05

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 ℝⁿ×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.

Cited by

• Strichartz estimates for higher order Schrödinger equations with Partial regular initial data
• Strichartz estimates involving orthonormal systems at the critical summability exponent
• Orthonormal Strichartz estimates for Dunkl-Schrödinger equation of initial data with Sobolev regularity

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