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Harmonic and monogenic potentials in low dimensional Euclidean half‐space
Author(s) -
Brackx F.,
De Bie H.,
De Schepper H.
Publication year - 2013
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.2956
Subject(s) - mathematics , euclidean space , dimension (graph theory) , harmonic function , euclidean geometry , boundary (topology) , mathematical analysis , logarithm , plane (geometry) , space (punctuation) , harmonic , chain (unit) , pure mathematics , euclidean distance , geometry , quantum mechanics , physics , philosophy , linguistics
In the framework of Clifford analysis, a chain of harmonic and monogenic potentials in the upper half of Euclidean spaceR m + 1was constructed recently, including a higher dimensional analogue of the logarithmic function in the complex plane. Their distributional limits at the boundaryR mwere 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. Copyright © 2013 John Wiley & Sons, Ltd.