Monogenic Gaussian distribution in closed form and the Gaussian fundamental solution

Abstract

In this article we present a closed formula for the CK-extension of the Gaussian distribution in ℝ ^m , and the monogenic version of the holomorphic function which is a fundamental solution of the generalized Cauchy–Riemann operator.

Keywords:

• Clifford analysis
• Fueter's theorem
• CK-extension

AMS Subject Classification::

• 30G35

Acknowledgement

D. Peña Peña was supported by a Post-Doctoral Grant of Fundacão para a Ciência e a Tecnologia (FCT), Portugal.