Abstract
In the framework of Clifford analysis, a chain of harmonic and monogenic potentials is constructed in the upper half of Euclidean space ℝm+1, including a higher dimensional generalization of the complex logarithmic function. Their distributional limits at the boundary ℝm 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.
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Brackx, F., De Bie, H. & De Schepper, H. On a Chain of Harmonic and Monogenic Potentials in Euclidean Half–space. Potential Anal 41, 613–645 (2014). https://doi.org/10.1007/s11118-013-9385-2
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DOI: https://doi.org/10.1007/s11118-013-9385-2