Spectrum and analytic functional calculus ...
Type de document :
Compte-rendu et recension critique d'ouvrage
DOI :
Titre :
Spectrum and analytic functional calculus in real and quaternionicframeworks: An overview
Auteur(s) :
Titre de la revue :
AIMS Mathematics
Éditeur :
AIMS Press
Date de publication :
2023-12-22
Mot(s)-clé(s) en anglais :
spectrum in real algebras
conjugation
real operators
quaternionic operators
analytic functional calculus
conjugation
real operators
quaternionic operators
analytic functional calculus
Discipline(s) HAL :
Mathématiques [math]
Résumé en anglais : [en]
An approach to the elementary spectral theory for quaternionic linear operators waspresented by the author in a recent paper, quoted and discussed in the Introduction, where, unlikein works by other authors, the construction ...
Lire la suite >An approach to the elementary spectral theory for quaternionic linear operators waspresented by the author in a recent paper, quoted and discussed in the Introduction, where, unlikein works by other authors, the construction of the analytic functional calculus used a Riesz-Dunford-Gelfand type kernel, and the spectra were defined in the complex plane. In fact, the present authorregards the quaternionic linear operators as a special class of real linear operators, a point of viewleading to a simpler and a more natural approach to them. The author’s main results in this frameworkare summarized in the following, and other pertinent comments and remarks are also included in thistext. In addition, a quaternionic joint spectrum for pairs of operators is discussed, and an analyticfunctional calculus which uses a Martinelli type kernel in two variables is recalled.Lire moins >
Lire la suite >An approach to the elementary spectral theory for quaternionic linear operators waspresented by the author in a recent paper, quoted and discussed in the Introduction, where, unlikein works by other authors, the construction of the analytic functional calculus used a Riesz-Dunford-Gelfand type kernel, and the spectra were defined in the complex plane. In fact, the present authorregards the quaternionic linear operators as a special class of real linear operators, a point of viewleading to a simpler and a more natural approach to them. The author’s main results in this frameworkare summarized in the following, and other pertinent comments and remarks are also included in thistext. In addition, a quaternionic joint spectrum for pairs of operators is discussed, and an analyticfunctional calculus which uses a Martinelli type kernel in two variables is recalled.Lire moins >
Langue :
Anglais
Vulgarisation :
Non
Collections :
Source :
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