Formulations of the F-functional calculus and some consequences

Formulations of the F-functional calculus and some consequences

In this paper we introduce the two possible formulations of the F-functional calculus that are based on the Fueter-Sce mapping theorem in integral form and we introduce the pseudo- F -resolvent equation. In the case of dimension 3 we prove the F -resolvent equation and we study the analogue of the R...

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Veröffentlicht in:Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 2016-06, Vol.146 (3), p.509-545
Hauptverfasser: Colombo, Fabrizio, Gantner, Jonathan
Format: Artikel
Sprache:eng
Schlagworte:
Analogue
Calculus
Formulations
Integrals
Mapping
Mathematical analysis
Projectors
Theorems
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Zusammenfassung:In this paper we introduce the two possible formulations of the F-functional calculus that are based on the Fueter-Sce mapping theorem in integral form and we introduce the pseudo- F -resolvent equation. In the case of dimension 3 we prove the F -resolvent equation and we study the analogue of the Riesz projectors associated with this calculus. The case of dimension 3 is also useful to study the quaternionic version of the F -functional calculus.
ISSN:0308-2105
1473-7124
DOI:10.1017/S0308210515000645