Quaternionic and Clifford Analysis for Non-smooth Domains

Ricardo Abreu-Blaya () and Juan Bory-Reyes ()
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Ricardo Abreu-Blaya: University of Holguin, Faculty of Mathematics and Informatics
Juan Bory-Reyes: Universidad de Oriente, Department of Mathematics

Chapter 50 in Operator Theory, 2015, pp 1447-1470 from Springer

Abstract: Abstract 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.

Keywords: Clifford Algebra; Real Banach Space; Hausdorff Measure; Monogenic Function; Jordan Domain (search for similar items in EconPapers)
Date: 2015
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-0348-0667-1_31

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DOI: 10.1007/978-3-0348-0667-1_31

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