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Harmonic and monogenic potentials in Euclidean half-space

Fred Brackx (UGent) , Hendrik De Bie (UGent) and Hennie De Schepper (UGent)
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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.
Keywords
potential theory, Clifford analysis

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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.
@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},
}

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