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

Research output: Contribution to journalArticleScientificpeer-review


Original languageEnglish
Pages (from-to)1-14
Number of pages14
JournalApplied Mathematics and Computation
Early online date2018
Publication statusPublished - 1 Apr 2019
Publication typeA1 Journal article-refereed


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.


  • Cauchy's formula, Hypermonogenic solution, Plane wave

Publication forum classification

Field of science, Statistics Finland