Restriction theorem for the Fourier-Dunkl transform. I: Cone surface. (English) Zbl 1505.42013
Summary: 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.
MSC:
| 42B10 | Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type |
| 47B10 | Linear operators belonging to operator ideals (nuclear, \(p\)-summing, in the Schatten-von Neumann classes, etc.) |
| 42B35 | Function spaces arising in harmonic analysis |
| 35P10 | Completeness of eigenfunctions and eigenfunction expansions in context of PDEs |
| 42C05 | Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis |
Keywords:
Dunkl Laplacian; Fourier-Dunkl transform; restriction theorem; orthonormal Strichartz inequalities; square root of Dunkl LaplacianReferences:
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