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

Formulations of the F-functional calculus and some consequences

COLOMBO, FABRIZIO;
2016-01-01

Abstract

In this paper we introduce the two possible formulations of the-functional calculus that are based on the Fueter-Sce mapping theorem in integral form and we introduce the pseudo-resolvent equation. In the case of dimension 3 we prove the-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-functional calculus.
2016
F-spectrum; formulations of the F-functional calculus for n-tuples of operators; Fueter-Sce mapping theorem in integral form; projectors; quaternionic F-resolvent equation; quaternionic version of the F-functional calculus; Mathematics (all)
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11311/1007248
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