Work

A local representation formula for quaternionic slice regular functions

Year: 2020

Type: article

Abstract: After their introduction in 2006, quaternionic slice regular functions have mostly been studied over domains that are symmetric with respect to the real axis. This choice was motivated by some foundational results published in 2009, such as the Representation Formula for axially symmetric domains. The present work studies slice regular functions over domains that are not axially symmetric, partly correcting the hypotheses of some previously published results. In particular, this work includes a Local Representation Formula valid without the symmetry hypothesis. Moreover, it determines a class of domains, called simple, having the following property: every slice regular function on a simple domain can be uniquely extended to the symmetric completion of its domain.

Source: Proceedings of the American Mathematical Society

DOI: 10.1090/proc/15339

Authors: Graziano Gentili, Caterina Stoppato

Institution: University of Florence

Language: English

Topic: Algebraic and Geometric Analysis

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: Istituto Nazionale di Alta Matematica "Francesco Severi", Ministero dell’Istruzione, dell’Università e della Ricerca, Gruppo Nazionale per le Strutture Algebriche, Geometriche e le loro Applicazioni

Award: G15967578