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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
