Bulletin of the Belgian Mathematical Society - Simon Stevin

The algebraic structure of quaternionic analysis

Massimo Tarallo

Full-text: Open access

Abstract

The regularity of a quaternionic function is reinterpreted through a new canonical decomposition of the real differential, giving new insights into the algebraic properties of the regularity itself. The result comes from a somewhat unusual point of view on the automorphisms of the quaternionic field: a general notion of quaternionic linearity is associated to them, and some unnoticed metric properties of their inner representation are used to build up the theory.

Article information

Source
Bull. Belg. Math. Soc. Simon Stevin, Volume 18, Number 4 (2011), 577-621.

Dates
First available in Project Euclid: 8 November 2011

Permanent link to this document
https://projecteuclid.org/euclid.bbms/1320763125

Digital Object Identifier
doi:10.36045/bbms/1320763125

Mathematical Reviews number (MathSciNet)
MR2907607

Zentralblatt MATH identifier
1253.30077

Subjects
Primary: 30G35: Functions of hypercomplex variables and generalized variables 32A30: Other generalizations of function theory of one complex variable (should also be assigned at least one classification number from Section 30) {For functions of several hypercomplex variables, see 30G35}

Keywords
Quaternionic analysis regular functions quaternionic linearity

Citation

Tarallo, Massimo. The algebraic structure of quaternionic analysis. Bull. Belg. Math. Soc. Simon Stevin 18 (2011), no. 4, 577--621. doi:10.36045/bbms/1320763125. https://projecteuclid.org/euclid.bbms/1320763125


Export citation