The uncertainty principle in Clifford analysis

TL;DR

This paper extends classical uncertainty principles, specifically Heisenberg's inequality and Hardy's theorem, to the Clifford-Fourier transform on Euclidean space, broadening their applicability in Clifford analysis.

Contribution

It introduces and proves uncertainty principles for the Clifford-Fourier transform, a novel extension of classical Fourier analysis results to Clifford analysis.

Findings

Heisenberg's inequality for Clifford-Fourier transform established

Hardy's theorem adapted to Clifford analysis

Provides foundational results for further research in Clifford analysis

Abstract

In this paper, we provide the Heisenberg's inequality and the Hardy's theorem for the Clifford-Fourier transform on $\mathbb{R}^m$.