Distributional Boundary Values of Harmonic Potentials in Euclidean Half-space as Fundamental Solutions of Convolution Operators in Clifford Analysis

2012/10/07 by Fred Brackx, Brackx, Fred, Hendrik De Bie +3 · 2 citations
Mathematics · #30G35 #31C45 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #math.CA #msc:30G35 #msc:31C45

paper · pdf · doi:10.48550/arxiv.1210.2389

arXiv admin note: text overlap with arXiv:1210.2044

arxiv created 2012/10/07 · arxiv updated 2012/10/10

Abstract

In the framework of Clifford analysis, a chain of harmonic and monogenic potentials in the upper half of Euclidean space \mR^m+1 was recently constructed, including a higher dimensional analogue of the logarithmic function in the complex plane. In this construction the distributional limits of these potentials at the boundary \mR^m are crucial. The remarkable relationship between these distributional boundary values and four basic pseudodifferential operators linked with the Dirac and Laplace operators is studied.

Citations

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

Cited by

• Harmonic and Monogenic Potentials in Low Dimensional Euclidean Half-Space
• Representation of Distributions by Harmonic and Monogenic Potentials in Euclidean Space

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