Higher order Borel-Pompeiu representations in Clifford analysis (Q2831022)

The authors show that a higher-order Borel-Pompeiu (Cauchy-Pompeiu) formula, relatively to an arbitrary orthogonal basis of a Euclidean space can be extended to the framework of generalized Clifford analysis. In lower-dimensional Clifford algebras, explicit expressions of the kernel functions are derived relatively to the corresponding structural sets. Properties of the fundamental solution of so-called iterated Cauchy-Riemann operators are studied. Classical concepts of Cauchy transforms are adapted to a collection of structural sets, which are very important in the theory of boundary value problems for partial differential equations.