The global Borel-Pompieu-type formula for quaternionic slice regular functions

J. Oscar González Cervantes; Daniel González-Campos

doi:10.1080/17476933.2020.1738410

The global Borel-Pompieu-type formula for quaternionic slice regular functions

J. Oscar González Cervantes, Daniel González-Campos

Escuela Superior de Física y Matemáticas (ESFM)

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

This paper presents the global Borel-Pompieu- and the global Cauchy-type integral formulas for the quaternionic slice regular functions using the relationship between this function space and a non-constant coefficient differential operator given by (Formula presented.) according to [González-Cervantes JO. On cauchy integral theorem for quaternionic slice regular functions. Complex Anal Oper Theory. 2019;13(6):2527–2539; Colombo F, González-Cervantes JO, Sabadini I. A non-constant coefficients differential operator associated to slice monogenic functions. Trans Am Math Soc. 2013;365:303–318]. This association allows to show a behavior of the theory of slice regular functions similar to the well known theories of the hypercomplex analysis.

Original language	English
Pages (from-to)	721-730
Number of pages	10
Journal	Complex Variables and Elliptic Equations
Volume	66
Issue number	5
DOIs	https://doi.org/10.1080/17476933.2020.1738410
State	Published - 2021

Keywords

I. Sabadini
Primary 30G35
Quaternions
non-constant coefficient differential operator
quaternionic Borel-Pompeiu formula
quaternionic Cauchy integral formula
quaternionic slice regular functions

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abstract = "This paper presents the global Borel-Pompieu- and the global Cauchy-type integral formulas for the quaternionic slice regular functions using the relationship between this function space and a non-constant coefficient differential operator given by (Formula presented.) according to [Gonz{\'a}lez-Cervantes JO. On cauchy integral theorem for quaternionic slice regular functions. Complex Anal Oper Theory. 2019;13(6):2527–2539; Colombo F, Gonz{\'a}lez-Cervantes JO, Sabadini I. A non-constant coefficients differential operator associated to slice monogenic functions. Trans Am Math Soc. 2013;365:303–318]. This association allows to show a behavior of the theory of slice regular functions similar to the well known theories of the hypercomplex analysis.",

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KW - Quaternions

KW - non-constant coefficient differential operator

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The global Borel-Pompieu-type formula for quaternionic slice regular functions

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Keywords

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