Higher order Borel-Pompeiu representations in Clifford analysis

摘要

In this paper, we show that a higher order Borel-Pompeiu (Cauchy-Pompeiu) formula, associated with an arbitrary orthogonal basis (called structural set) of a Euclidean space, can be extended to the framework of generalized Clifford analysis. Furthermore, in lower dimensional cases, as well as for combinations of standard structural sets, explicit expressions of the kernel functions are derived. Copyright (c) 2015 John Wiley & Sons, Ltd.