Quaternionic Analysis and Some Conventional Theories

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

Chapter 55 in Operator Theory, 2026, pp 1767-1790 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.

Date: 2026
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-032-16356-1_25

Ordering information: This item can be ordered from
http://www.springer.com/9783032163561

DOI: 10.1007/978-3-032-16356-1_25

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().