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Open AccessArticle

Explicit Formulas for All Scator Holomorphic Functions in the (1+2)-Dimensional Case

Wydział Fizyki, Uniwersytet w Białymstoku, ul. Ciołkowskiego 1L, 15-245 Białystok, Poland
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Symmetry 2020, 12(9), 1550; https://doi.org/10.3390/sym12091550
Received: 10 August 2020 / Revised: 14 September 2020 / Accepted: 16 September 2020 / Published: 20 September 2020
(This article belongs to the Special Issue Symmetry in Geometric Functions and Mathematical Analysis)
Scators form a vector space endowed with a non-distributive product, in the hyperbolic case, have physical applications related to some deformations of special relativity (breaking the Lorentz symmetry) while the elliptic case leads to new examples of hypercomplex numbers and related notions of holomorphicity. Until now, only a few particular cases of scator holomorphic functions have been found. In this paper we obtain all solutions of the generalized Cauchy–Riemann system which describes analogues of holomorphic functions in the (1+2)-dimensional scator space. View Full-Text
Keywords: scators; holomorphic functions; generalized Cauchy–Riemann equations scators; holomorphic functions; generalized Cauchy–Riemann equations
MDPI and ACS Style

Cieśliński, J.L.; Zhalukevich, D. Explicit Formulas for All Scator Holomorphic Functions in the (1+2)-Dimensional Case. Symmetry 2020, 12, 1550.

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