<div class="csl-bib-body">
<div class="csl-entry">Gantner, J. (2018). <i>Slice hyperholomorphic functions and the quaternionic functional calculus</i> [Diploma Thesis, Technische Universität Wien]. reposiTUm. https://doi.org/10.34726/hss.2018.23470</div>
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dc.identifier.uri
https://doi.org/10.34726/hss.2018.23470
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dc.identifier.uri
http://hdl.handle.net/20.500.12708/3027
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dc.description
Arbeit an der Bibliothek noch nicht eingelangt - Daten nicht geprueft
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dc.description
Abweichender Titel nach Übersetzung der Verfasserin/des Verfassers
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dc.description.abstract
The discovery of slice hyperholomorphic functions gave great impact to the field of quaternionic functional analysis. Based on this notion of generalized holomorphicity, it was possible to develop the analogue of the Riesz-Dunford functional calculus for quaternionic linear operators. In the present master thesis an overview on the theory of quaternion-valued slice hyperholomorphic functions and the associated S-functional calculus for quaternionic linear operators is given. The author treats the relation to classical holomorphicity and shows the two main tools for working with these functions: the Splitting Lemma and the Representation Formula. Furthermore, he proves the generalizations of certain classical results, which are necessary to define the S-functional calculus: slice hyperholomorphic functions allow a power series expansion at points on the real axis and they satisfy a Runge-type approximation theorem as well as an integral formula of Cauchy-type with a modified kernel. In the second half of the thesis, the notion of S-spectrum and the S-functional calculus is defined, which is based on this notion of spectrum for quaternionic linear operators. Their main properties such as the boundedness of the S-spectrum, the Spectral Mapping Theorem and compatibility of the S-functional calculus with algebraic operations and uniform limits are proven. In particular, the analogue of the classical resolvent equation is shown and proofs of the product rule and for the existence of Riesz-projectors, which are based on this equation, are given.
en
dc.language
English
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dc.language.iso
en
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dc.rights.uri
http://rightsstatements.org/vocab/InC/1.0/
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dc.subject
Slice hyperholomorphe Funktionen
de
dc.subject
Funktionalkalkül
de
dc.subject
Slice hyperholomorphic functions
en
dc.subject
functional calculus
en
dc.title
Slice hyperholomorphic functions and the quaternionic functional calculus
en
dc.title.alternative
Slice hyperholomorphe Funktionen und der quaternionische Funktionalkalkül
de
dc.type
Thesis
en
dc.type
Hochschulschrift
de
dc.rights.license
In Copyright
en
dc.rights.license
Urheberrechtsschutz
de
dc.identifier.doi
10.34726/hss.2018.23470
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dc.contributor.affiliation
TU Wien, Österreich
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dc.rights.holder
Jonathan Gantner
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dc.publisher.place
Wien
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tuw.version
vor
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tuw.thesisinformation
Technische Universität Wien
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tuw.publication.orgunit
E101 - Institut für Analysis und Scientific Computing
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dc.type.qualificationlevel
Diploma
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dc.identifier.libraryid
AC14532230
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dc.description.numberOfPages
90
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dc.identifier.urn
urn:nbn:at:at-ubtuw:1-106769
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dc.thesistype
Diplomarbeit
de
dc.thesistype
Diploma Thesis
en
dc.rights.identifier
In Copyright
en
dc.rights.identifier
Urheberrechtsschutz
de
tuw.advisor.staffStatus
staff
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item.fulltext
with Fulltext
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item.grantfulltext
open
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item.cerifentitytype
Publications
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item.cerifentitytype
Publications
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item.languageiso639-1
en
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item.openairecristype
http://purl.org/coar/resource_type/c_18cf
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item.openairecristype
http://purl.org/coar/resource_type/c_18cf
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item.openairetype
Thesis
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item.openairetype
Hochschulschrift
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item.openaccessfulltext
Open Access
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crisitem.author.dept
E104 - Institut für Diskrete Mathematik und Geometrie