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Title: Fractional powers of linear operators in locally convex vector spaces
Language: English
Authors: Meichsner, Jan 
Keywords: Functional Analysis;Locally Convex Spaces;Functional Calculus;Fractional Powers;Caffarelli-Silvestre Extension
Issue Date: 2021
Examination Date: 25-Feb-2021
Abstract (german): 
Die Arbeit widmet sich der Untersuchung nicht-negativer Operatoren in lokalkonvexen Räumen. Es werden zunächst grundlegende Eigenschaften untersucht und anschließend ein Funktionalkalkül für die Operatorenklasse konstruiert. Mit Hilfe des Kalküls werden fraktionelle Potenzen, eine wichtige im Kalkül enthaltene Funktionenklasse, studiert. Abschließend wird die Theorie auf das Caffarelli-Silvestre Problem angewandt.
Abstract (english): 
The work is dedicated to the study of non-negative operators in locally convex spaces. At the beginning basic properties of this class of operators are investigated and afterwards a functional calculus is constructed. With its help, fractional powers, an important class of functions contained in the calculus, are investigated. At the end the theory is applied to the Caffarelli-Silvestre problem.
DOI: 10.15480/882.3674
Institute: Mathematik E-10 
Document Type: Thesis
Thesis Type: Doctoral Thesis
Advisor: Lindner, Marko  
Referee: Seifert, Christian  
ter Elst, Tom 
License: CC BY 4.0 (Attribution) CC BY 4.0 (Attribution)
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