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

TL;DR

This paper extends the Fourier transform to the Fourier-Dunkl transform, proving a restriction theorem for cone surfaces and deriving related Strichartz inequalities, advancing harmonic analysis in this generalized setting.

Contribution

It introduces the Fourier-Dunkl transform, establishes a restriction theorem for cone surfaces, and applies it to derive Strichartz inequalities for Dunkl Laplacian.

Findings

Proved restriction theorem for Fourier-Dunkl transform on cone surfaces

Generalized restriction theorem to orthonormal functions

Derived Strichartz inequalities for Dunkl Laplacian

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.