Hostname: page-component-cd9895bd7-q99xh Total loading time: 0 Render date: 2024-12-28T04:18:02.708Z Has data issue: false hasContentIssue false
  • English
  • Français

Formulations of the -functional calculus and some consequences

Part of: General theory of linear operators

Published online by Cambridge University Press:  05 May 2016

Fabrizio Colombo  and
Jonathan Gantner
Fabrizio Colombo
Affiliation:
Politecnico di Milano, Dipartimento di Matematica, Via E. Bonardi 9, 20133 Milano, Italy ([email protected]; [email protected])
Jonathan Gantner
Affiliation:
Politecnico di Milano, Dipartimento di Matematica, Via E. Bonardi 9, 20133 Milano, Italy ([email protected]; [email protected])
Get access Rights & Permissions [Opens in a new window]

Extract

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.

Keywords

Fueter–Sce mapping theorem in integral form-spectrumformulations of the -functional calculus for n-tuples of operatorsprojectorsquaternionic version of the -functional calculusquaternionic -resolvent equation

MSC classification

Secondary: 47A10: Spectrum, resolvent 47A60: Functional calculus
Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 146 , Issue 3 , June 2016 , pp. 509 - 545
Copyright
Copyright © Royal Society of Edinburgh 2016 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)