1. Harmonic and Monogenic Potentials in Euclidean Halfspace.
- Author
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Brackx, F., De Bie, H., and De Schepper, H.
- Subjects
- *
HARMONIC functions , *MONOGENIC functions , *EUCLIDEAN distance , *CLIFFORD algebras , *DIRAC function , *LAPLACE'S equation - Abstract
In the framework of Clifford analysis a chain of harmonic and monogenic potentials is constructed in the upper half of Euclidean space Rm+1 Their distributional limits at the boundary are computed, obtaining in this way well-known distributions in Rm 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. [ABSTRACT FROM AUTHOR]
- Published
- 2011
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