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Harmonic and monogenic potentials in Euclidean half-space

Fred Brackx UGent, Hendrik De Bie UGent and Hennie De Schepper UGent (2011) 9th international conference on numerical analysis and applied mathematics, Proceedings. 1389.
abstract
In the framework of Clifford analysis a chain of harmonic and monogenic potentials is constructed in the upper half of Euclidean space R^m+1. Their distributional limits at the boundary are computed, obtaining in this way well-known distributions in R^m such as the Dirac distribution, the Hilbert kernel, 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.
Please use this url to cite or link to this publication:
author
organization
year
type
conference
publication status
published
subject
keyword
potential theory, Clifford analysis
in
9th international conference on numerical analysis and applied mathematics, Proceedings
editor
Teodore Simos
volume
1389
pages
5 pages
publisher
AIP Conference Proceedings
conference name
9th International Conference on Numerical analysis and Applied Mathematics (ICNAAM - 2012)A
conference location
Halkidiki, Greece
conference start
2011-09-19
conference end
2011-09-25
DOI
10.1063/1.3636717
language
English
UGent publication?
yes
classification
C1
copyright statement
I have transferred the copyright for this publication to the publisher
id
2154848
handle
http://hdl.handle.net/1854/LU-2154848
date created
2012-06-15 11:54:25
date last changed
2016-12-19 15:37:06
@inproceedings{2154848,
  abstract     = {In the framework of Clifford analysis a chain of harmonic and monogenic potentials is constructed in the upper
half of Euclidean space R\^{ }m+1. Their distributional limits at the boundary are computed, obtaining in this way well-known distributions in R\^{ }m such as the Dirac distribution, the Hilbert kernel, 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.},
  author       = {Brackx, Fred and De Bie, Hendrik and De Schepper, Hennie},
  booktitle    = {9th international conference on numerical analysis and applied mathematics, Proceedings},
  editor       = {Simos, Teodore},
  keyword      = {potential theory,Clifford analysis},
  language     = {eng},
  location     = {Halkidiki, Greece},
  pages        = {5},
  publisher    = {AIP Conference Proceedings},
  title        = {Harmonic and monogenic potentials in Euclidean half-space},
  url          = {http://dx.doi.org/10.1063/1.3636717},
  volume       = {1389},
  year         = {2011},
}

Chicago
Brackx, Fred, Hendrik De Bie, and Hennie De Schepper. 2011. “Harmonic and Monogenic Potentials in Euclidean Half-space.” In 9th International Conference on Numerical Analysis and Applied Mathematics, Proceedings, ed. Teodore Simos. Vol. 1389. AIP Conference Proceedings.
APA
Brackx, Fred, De Bie, H., & De Schepper, H. (2011). Harmonic and monogenic potentials in Euclidean half-space. In Teodore Simos (Ed.), 9th international conference on numerical analysis and applied mathematics, Proceedings (Vol. 1389). Presented at the 9th International Conference on Numerical analysis and Applied Mathematics (ICNAAM - 2012)A, AIP Conference Proceedings.
Vancouver
1.
Brackx F, De Bie H, De Schepper H. Harmonic and monogenic potentials in Euclidean half-space. In: Simos T, editor. 9th international conference on numerical analysis and applied mathematics, Proceedings. AIP Conference Proceedings; 2011.
MLA
Brackx, Fred, Hendrik De Bie, and Hennie De Schepper. “Harmonic and Monogenic Potentials in Euclidean Half-space.” 9th International Conference on Numerical Analysis and Applied Mathematics, Proceedings. Ed. Teodore Simos. Vol. 1389. AIP Conference Proceedings, 2011. Print.