Beurling's theorem for the Clifford-Fourier transform

TL;DR

This paper extends Beurling's theorem to the Clifford-Fourier transform and derives analogues of classical theorems like Hardy, Cowling-Price, and Gelfand-Shilov within Clifford analysis, broadening the theoretical framework.

Contribution

It introduces a generalized Beurling's theorem for the Clifford-Fourier transform and establishes related classical theorems in the context of Clifford analysis.

Findings

Generalization of Beurling's theorem for Clifford-Fourier transform

Analogues of Hardy, Cowling-Price, and Gelfand-Shilov theorems in Clifford analysis

Enhanced understanding of harmonic analysis in Clifford algebra setting

Abstract

We give a generalization of Beurling's theorem for the Clifford-Fourier transform. Then, analogues of Hardy, Cowling-Price and Gelfand-Shilov theorems are obtained in Clifford analysis.