Monogenic Gaussian distribution in closed form and the Gaussian fundamental solution

TL;DR

This paper derives a closed-form expression for the CK-extension of Gaussian distributions and introduces a monogenic version of a fundamental holomorphic function, advancing the mathematical understanding of these functions in Clifford analysis.

Contribution

It provides the first explicit closed-form formula for the CK-extension of Gaussian distributions and constructs a monogenic analogue of a key holomorphic function.

Findings

Closed-form CK-extension of Gaussian distribution in $\

Monogenic version of $rac{ ext{exp}(z^2/2)}{z}$ as a fundamental solution.

Enhanced mathematical tools for Clifford analysis and potential applications in higher-dimensional function theory.

Abstract

In this paper we present a closed formula for the CK-extension of the Gaussian distribution in $\mathbb R^m$, and the monogenic version of the holomorphic function $\exp(z^2/2)/z$ which is a fundamental solution of the generalized Cauchy-Riemann operator.