Harmonic and Monogenic Potentials in Low Dimensional Euclidean Half-Space

2012/12/08 by Fred Brackx, Brackx, Fred, Hendrik De Bie +3
Mathematics · #30G35 #31B05 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #math.CA #msc:30G35 #msc:31B05

paper · pdf · doi:10.48550/arxiv.1212.1766

arXiv admin note: substantial text overlap with arXiv:1210.2389, arXiv:1210.2044

arxiv created 2012/12/08 · arxiv updated 2012/12/11

Abstract

In the framework of Clifford analysis, a chain of harmonic and monogenic potentials in the upper half of Euclidean space R^m+1 was constructed recently, including a higher dimensional analogue of the logarithmic function in the complex plane. Their distributional limits at the boundary R^m were also determined. In this paper the potentials and their distributional boundary values are calculated in dimensions 3 and 4, dimensions for which the expressions in general dimension break down.

Citations

• Distributional Boundary Values of Harmonic Potentials in Euclidean Half-space as Fundamental Solutions of Convolution Operators in Clifford Analysis
• On a Chain of Harmonic and Monogenic Potentials in Euclidean Half-space

Related

• Representation of Distributions by Harmonic and Monogenic Potentials in Euclidean Space
• On a Chain of Harmonic and Monogenic Potentials in Euclidean Half-space
• Distributional Boundary Values of Harmonic Potentials in Euclidean Half-space as Fundamental Solutions of Convolution Operators in Clifford Analysis
• Two Families of Clifford Distributions Revisited
• On a Riemann-Hilbert boundary value problem for (φ,ψ)-harmonic functions in ℝ^m