Hypermonogenic solutions and plane waves of the Dirac operator in Rp×Rq

Alí Guzmán Adán, Heikki Orelma and Franciscus Sommen

Applied Mathematics and Computation, 2019, vol. 346, issue C, 1-14

Abstract: In this paper we first define hypermonogenic solutions of the Dirac operator in Rp×Rq and study some basic properties, e.g., obtaining a Cauchy integral formula in the unit hemisphere. Hypermonogenic solutions form a natural function class in classical Clifford analysis. After that, we define the corresponding hypermonogenic plane wave solutions and deduce explicit methods to compute these functions.

Keywords: Hypermonogenic solution; Cauchy’s formula; Plane wave (search for similar items in EconPapers)
Date: 2019
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:346:y:2019:i:c:p:1-14

DOI: 10.1016/j.amc.2018.09.058

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