Clifford Fourier-Mellin transform with two real square roots of -1 in Cl(p,q), p+q=2

TL;DR

This paper introduces a non-commutative Clifford Fourier-Mellin transform for signal functions valued in Clifford algebras with p+q=2, extending classical Fourier analysis to a broader algebraic context.

Contribution

It presents a novel generalization of the Fourier-Mellin transform within Clifford algebra, specifically for Cl(p,q) with p+q=2, incorporating two real square roots of -1.

Findings

Generalization of Fourier-Mellin transform to Clifford algebra

Applicable to signals in Cl(p,q) with p+q=2

Provides a framework for non-commutative Fourier analysis

Abstract

We describe a non-commutative generalization of the complex Fourier-Mellin transform to Clifford algebra valued signal functions over the domain $\R^{p,q}$ taking values in Cl(p,q), p+q=2. Keywords: algebra, Fourier transforms; Logic, set theory, and algebra, Fourier analysis, Integral transforms