Bulletin of the Belgian Mathematical Society - Simon Stevin

The algebraic structure of quaternionic analysis

Massimo Tarallo

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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

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

First available in Project Euclid: 8 November 2011

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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}

Quaternionic analysis regular functions quaternionic linearity


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

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