Spectrum and Analytic Functional Calculus for Clifford Operators via Stem Functions

The main purpose of this work is the construction of an analytic functional calculus for Clifford operators, which are operators acting on certain modules over Clifford algebras. Unlike in some preceding works by other authors, we use a spectrum defined in the complex plane, and also certain stem fu...

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Autor principal:	Vasilescu Florian-Horia
Formato:	article
Lenguaje:	EN
Publicado:	De Gruyter 2021
Materias:	clifford algebras stem functions analytic functional calculus clifford and complex spectra 30g35 30a05 47a10 47a60 Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/21e9a87cc6134fc69ef8953db59a82ef
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spelling	oai:doaj.org-article:21e9a87cc6134fc69ef8953db59a82ef2021-12-05T14:10:45ZSpectrum and Analytic Functional Calculus for Clifford Operators via Stem Functions2299-328210.1515/conop-2020-0115https://doaj.org/article/21e9a87cc6134fc69ef8953db59a82ef2021-07-01T00:00:00Zhttps://doi.org/10.1515/conop-2020-0115https://doaj.org/toc/2299-3282The main purpose of this work is the construction of an analytic functional calculus for Clifford operators, which are operators acting on certain modules over Clifford algebras. Unlike in some preceding works by other authors, we use a spectrum defined in the complex plane, and also certain stem functions, analytic in neighborhoods of such a spectrum. The replacement of the slice regular functions, having values in a Clifford algebra, by analytic stem functions becomes possible because of an isomorphism induced by a Cauchy type transform, whose existence is proved in the first part of this work.Vasilescu Florian-HoriaDe Gruyterarticleclifford algebrasstem functionsanalytic functional calculusclifford and complex spectra30g3530a0547a1047a60MathematicsQA1-939ENConcrete Operators, Vol 8, Iss 1, Pp 90-113 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	clifford algebras stem functions analytic functional calculus clifford and complex spectra 30g35 30a05 47a10 47a60 Mathematics QA1-939
spellingShingle	clifford algebras stem functions analytic functional calculus clifford and complex spectra 30g35 30a05 47a10 47a60 Mathematics QA1-939 Vasilescu Florian-Horia Spectrum and Analytic Functional Calculus for Clifford Operators via Stem Functions
description	The main purpose of this work is the construction of an analytic functional calculus for Clifford operators, which are operators acting on certain modules over Clifford algebras. Unlike in some preceding works by other authors, we use a spectrum defined in the complex plane, and also certain stem functions, analytic in neighborhoods of such a spectrum. The replacement of the slice regular functions, having values in a Clifford algebra, by analytic stem functions becomes possible because of an isomorphism induced by a Cauchy type transform, whose existence is proved in the first part of this work.
format	article
author	Vasilescu Florian-Horia
author_facet	Vasilescu Florian-Horia
author_sort	Vasilescu Florian-Horia
title	Spectrum and Analytic Functional Calculus for Clifford Operators via Stem Functions
title_short	Spectrum and Analytic Functional Calculus for Clifford Operators via Stem Functions
title_full	Spectrum and Analytic Functional Calculus for Clifford Operators via Stem Functions
title_fullStr	Spectrum and Analytic Functional Calculus for Clifford Operators via Stem Functions
title_full_unstemmed	Spectrum and Analytic Functional Calculus for Clifford Operators via Stem Functions
title_sort	spectrum and analytic functional calculus for clifford operators via stem functions
publisher	De Gruyter
publishDate	2021
url	https://doaj.org/article/21e9a87cc6134fc69ef8953db59a82ef
work_keys_str_mv	AT vasilescuflorianhoria spectrumandanalyticfunctionalcalculusforcliffordoperatorsviastemfunctions
_version_	1718371780134961152

Spectrum and Analytic Functional Calculus for Clifford Operators via Stem Functions

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