Abstract
In the framework of Clifford analysis, a chain of harmonic and monogenic potentials in the upper half of Euclidean space ℝm+1 was recently constructed, including a higher dimensional analogue of the logarithmic function in the complex plane. In this construction the distributional limits of these potentials at the boundary ℝm are crucial. The remarkable relationship between these distributional boundary values and four basic pseudodifferential operators linked with the Dirac and Laplace operators is studied.
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Brackx, F., De Bie, H., De Schepper, H. (2013). Distributional Boundary Values of Harmonic Potentials in Euclidean Half-Space as Fundamental Solutions of Convolution Operators in Clifford Analysis. In: Gentili, G., Sabadini, I., Shapiro, M., Sommen, F., Struppa, D. (eds) Advances in Hypercomplex Analysis. Springer INdAM Series, vol 1. Springer, Milano. https://doi.org/10.1007/978-88-470-2445-8_2
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DOI: https://doi.org/10.1007/978-88-470-2445-8_2
Publisher Name: Springer, Milano
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