Quaternionic and Clifford Analysis for Non-smooth Domains

Ricardo Abreu Blaya () and Juan Bory Reyes ()
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Ricardo Abreu Blaya: Universidad Autónoma de Guerrero, Facultad de Matemáticas
Juan Bory Reyes: Instituto Politécnico Nacional, SEPI, ESIME-Zacatenco

Chapter 58 in Operator Theory, 2026, pp 1839-1870 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 both 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 the interior and exterior of the domain vanishes at infinity and has a prescribed jump across the boundary.

Keywords: Clifford analysis; Quaternionic analysis; Cauchy transforms; Boundary value problems; Non-smooth domains; Fractals; 30G35; 28A80; 30G30; 30E20; 30E25 (search for similar items in EconPapers)
Date: 2026
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DOI: 10.1007/978-3-032-16356-1_31

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