Distributional boundary values of harmonic potentials in Euclidean half-space as fundamental solutions of convolution operators in Clifford analysis

Abstract

In the framework of Clifford analysis, a chain of harmonic and monogenic potentials in the upper half of Euclidean space ℝ m+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 ℝ m are crucial. The remarkable relationship between these distributional boundary values and four basic pseudodifferential operators linked with the Dirac and Laplace operators is studied