Higher order Borel-Pompeiu representations in Clifford analysis

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• 作者：Juan Bory Reyes ; Hennie De Schepper ; Alí ; Guzmá ; n Adá ; n and Frank Sommen
• 刊名：Mathematical Methods in the Applied Sciences
• 出版年：2016
• 出版时间：15 November 2016
• 年：2016
• 卷：39
• 期：16
• 页码：4787-4796
• 全文大小：188K
• ISSN：1099-1476

文摘

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