Quaternionic Analysis and Some Conventional Theories

Michael Shapiro ()
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Michael Shapiro: Escuela Superior de Física y Matemáticas, del Instituto Politécnico Nacional, Departamento de Matemáticas

Chapter 49 in Operator Theory, 2015, pp 1423-1446 from Springer

Abstract: Abstract Firstly, it is recalled briefly what are the analogues of the usual Cauchy–Riemann operators of complex analysis for quaternion-valued functions. Two of them, the Fueter and the Moisil–Théodoresco operators, are related to the Laplace equation, and one more is related to the Helmholtz operator. Secondly, it is shown that each of the following four theories can be embedded into one of the above quaternionic ones: holomorphic functions in ℂ 2 $$\mathbb{C}^{2}$$ , vector analysis, time-harmonic electromagnetic, and time-harmonic spinor fields. It is illustrated with specific examples that such embeddings prove to be rather fruitful for the conventional theories.

Keywords: Vector Field; Holomorphic Function; Conventional Theory; Quaternionic Multiplication; Cauchy Integral Formula (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_25

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DOI: 10.1007/978-3-0348-0667-1_25

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