Potential Analysis

, Volume 41, Issue 2, pp 613–645 | Cite as

On a Chain of Harmonic and Monogenic Potentials in Euclidean Half–space



In the framework of Clifford analysis, a chain of harmonic and monogenic potentials is constructed in the upper half of Euclidean space ℝ m+1, including a higher dimensional generalization of the complex logarithmic function. Their distributional limits at the boundary ℝ m turn out to be well-known distributions such as the Dirac distribution, the Hilbert kernel, the fundamental solution of the Laplace and Dirac operators, the square root of the negative Laplace operator, and the like. It is shown how each of those potentials may be recovered from an adjacent kernel in the chain by an appropriate convolution with such a distributional limit.


Monogenic potential Harmonic potential 

Mathematics Subject Classification



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© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  1. 1.Clifford Research Group, Department of Mathematical Analysis, Faculty of Engineering and ArchitectureGhent UniversityGentBelgium

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