English

Harmonic and Monogenic Potentials in Low Dimensional Euclidean Half-Space

Classical Analysis and ODEs 2012-12-11 v1

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.

Keywords

Cite

@article{arxiv.1212.1766,
  title  = {Harmonic and Monogenic Potentials in Low Dimensional Euclidean Half-Space},
  author = {Fred Brackx and Hendrik De Bie and Hennie De Schepper},
  journal= {arXiv preprint arXiv:1212.1766},
  year   = {2012}
}

Comments

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

R2 v1 2026-06-21T22:50:44.547Z