# Donoho-Stark's Uncertainty Principles in Real Clifford Algebras

## TL;DR

This paper extends uncertainty principles, including Donoho-Stark's, to real Clifford algebras using the Clifford Fourier transform, broadening the mathematical framework for analysis in Clifford analysis.

## Contribution

It establishes several uncertainty inequalities and qualitative principles within real Clifford algebras, enhancing the theoretical foundation of Clifford analysis.

## Key findings

- Proved Hausdorf-Young inequality in Clifford algebra
- Established Donoho-Stark uncertainty principles in Clifford context
- Extended uncertainty principles to real Clifford algebras

## Abstract

The Clifford Fourier transform (CFT) has been shown to be a powerful tool in the Clifford analysis. In this work, several uncertainty inequalities are established in the real Clifford algebra $Cl_{(p,q)}$, \ including the Hausdorf-Young inequality, and three qualitative uncertainty principles of Donoho-Stark.