On Some Quaternionic Generalized Slice Regular Functions

The quaternionic valued functions of a quaternionic variable, often referred to as slice regular functions, has been studied extensively due to the large number of generalized results of the theory of one complex variable. Recently, several global properties of these functions has been found such as...

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Vydáno v:Advances in applied Clifford algebras Ročník 32; číslo 3
Hlavní autor: Cervantes, J. Oscar González
Médium: Journal Article
Jazyk:angličtina
Vydáno: Cham Springer International Publishing 01.07.2022
Springer Nature B.V
Témata:
Analytic functions
Applications of Mathematics
Complex variables
Differential equations
Mathematical and Computational Physics
Mathematical Methods in Physics
Operators (mathematics)
Physics
Physics and Astronomy
Theorems
Theoretical
Primary 30G35
Representation Theorem
Quaternionic generalized slice regular functions
Splitting Lemma
quaternionic Borel–Pompeiu formula
Quaternionic non-constant coefficient differential operator
ISSN:0188-7009, 1661-4909
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Popis
Shrnutí:The quaternionic valued functions of a quaternionic variable, often referred to as slice regular functions, has been studied extensively due to the large number of generalized results of the theory of one complex variable. Recently, several global properties of these functions has been found such as a Borel–Pompieu formula and a Stokes’ Theorem from the study of a differential operator, see González-Cervantes and González-Campos (Complex Var Ellipt Equ 66(5):1–10, 2021, https://doi.org/10.1080/17476933.2020.1738410 ). The aim of this paper is to present a kind of quaternionic generalized slice regular functions that on slices coincide with pairs of complex generalized holomorphic functions associated to Vekua problems. The global properties of these functions are obtained from a perturbed global-type operator and among their local properties presented in this work are the versions of Splitting Lemma, Representation Theorem and a conformal property.
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ISSN:0188-7009
1661-4909
DOI:10.1007/s00006-022-01219-x