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.
The algebraic structure of quaternionic analysis / M. Tarallo. - In: BULLETIN OF THE BELGIAN MATHEMATICAL SOCIETY SIMON STEVIN. - ISSN 1370-1444. - 18:4(2011), pp. 577-621.
The algebraic structure of quaternionic analysis
M. TaralloPrimo
2011
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.
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