A sharp Clifford-wavelet Heisenberg-type uncertainty principle

TL;DR

This paper develops a new, sharp Heisenberg-type uncertainty principle within the Clifford wavelet transform framework, extending uncertainty principles to Clifford analysis and providing precise mathematical bounds.

Contribution

It introduces a novel uncertainty principle for Clifford wavelet transforms, advancing the mathematical understanding of uncertainty in Clifford analysis.

Findings

Derived a sharp Heisenberg-type uncertainty inequality for Clifford wavelet transform.

Extended classical uncertainty principles to the Clifford analysis framework.

Provided rigorous mathematical formulation and proof of the new principle.

Abstract

In the present work we are concerned with the development of a new uncertainty principle based on wavelet transform in the Clifford analysis/algebras framework. We precisely derive a sharp Heisenberg-type uncertainty principle for the continuous Clifford wavelet transform.