Clifford analysis, which covers a great part of the quaternionic analysis, is known as the theory of monogenic functions and represents a refinement of classical harmonic analysis and a generalization of complex analysis to higher dimensions. In this chapter a condensed account is given of a selection of studies connected to the Cauchy transform on the non-smooth boundary of a bounded domain in Euclidean space, in a Clifford and quaternionic analysis context. Particular emphasis will be placed on the study of the so-called jump problem (reconstruction problem) for monogenic functions, that is, the problem of reconstructing a monogenic function in both the interior and exterior of the domain vanishes at infinity and has a prescribed jump across the boundary.
CITATION STYLE
Abreu-Blaya, R., & Bory-Reyes, J. (2015). Quaternionic and clifford analysis for non-smooth domains. In Operator Theory (Vol. 2–2, pp. 1447–1470). Springer Basel. https://doi.org/10.1007/978-3-0348-0667-1_31
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