The aim of this paper is to extend the so called slice analysis to a general case in which the codomain is a real vector space of even dimension, i.e. is of the form R2n. This is a new setting which contains and encompasses in a nontrivial way other cases already studied in the literature and which requires new tools. To this end, we define a cone WCd in [End(R2n)]d and we extend the slice topology τs to this cone. Slice regular functions can be defined on open sets in (τs,WCd) and a number of results can be proved in this framework, among which a representation formula. This theory can be applied to some real algebras, called left slice complex structure algebras. These algebras include quaternions, octonions, Clifford algebras and real alternative ∗ -algebras but also left-alternative algebras and sedenions, thus providing brand new settings in slice analysis.

A representation formula for slice regular functions over slice-cones in several variables

Sabadini I.
2023-01-01

Abstract

The aim of this paper is to extend the so called slice analysis to a general case in which the codomain is a real vector space of even dimension, i.e. is of the form R2n. This is a new setting which contains and encompasses in a nontrivial way other cases already studied in the literature and which requires new tools. To this end, we define a cone WCd in [End(R2n)]d and we extend the slice topology τs to this cone. Slice regular functions can be defined on open sets in (τs,WCd) and a number of results can be proved in this framework, among which a representation formula. This theory can be applied to some real algebras, called left slice complex structure algebras. These algebras include quaternions, octonions, Clifford algebras and real alternative ∗ -algebras but also left-alternative algebras and sedenions, thus providing brand new settings in slice analysis.
2023
Alternative algebras
Clifford algebras
Functions of hypercomplex variable
Octonions
Quaternions
Representation formula
Slice regular functions
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11311/1256459
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