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Quaternionic and Clifford Analysis for Non-smooth Domains

In: Operator Theory

Author

Listed:
  • Ricardo Abreu-Blaya

    (University of Holguin, Faculty of Mathematics and Informatics)

  • Juan Bory-Reyes

    (Universidad de Oriente, Department of Mathematics)

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.

Suggested Citation

  • Ricardo Abreu-Blaya & Juan Bory-Reyes, 2015. "Quaternionic and Clifford Analysis for Non-smooth Domains," Springer Books, in: Daniel Alpay (ed.), Operator Theory, edition 127, chapter 50, pages 1447-1470, Springer.
    • Handle: RePEc:spr:sprchp:978-3-0348-0667-1_31
    DOI: 10.1007/978-3-0348-0667-1_31
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