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Master's Dissertation
DOI
10.11606/D.45.2014.tde-07032015-154510
Document
Author
Full name
Rodrigo Augusto Higo Mafra Cabral
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Paulo, 2014
Supervisor
Committee
Melo, Severino Toscano do Rego (President)
Forger, Frank Michael
Oliveira, Cesar Rogerio de
Title in Portuguese
O teorema espectral e a propriedade de "self-adjointness" para alguns operadores de Schrödinger
Keywords in Portuguese
"Self-adjointness"
C*-álgebras
Desigualdade de Kato
Kato-Rellich
Schrödinger
Teorema Espectral
Abstract in Portuguese
Neste texto são demonstrados, a partir do ponto de vista da teoria dos espaços de Hilbert e da teoria das C*-álgebras, teoremas relacionados a operadores auto-adjuntos em espaços de Hilbert, entre os quais estão o Teorema Espectral, o teorema de Kato-Rellich e a desigualdade de Kato. Também são dadas aplicações destes teoremas a alguns operadores de Schrödinger provenientes da Física-Matemática.
Title in English
The spectral theorem and the self-adjointness property for some Schrödinger operators
Keywords in English
C*-algebras
Kato's inequality
Kato-Rellich
Schrödinger
Self-adjointness
Spectral theorem
Abstract in English
In this text we prove, within the Hilbert spaces theory and C*-algebras points of view, some theorems which are related to self-adjoint operators acting on Hilbert spaces, among which are the Spectral Theorem, the Kato-Rellich theorem and Kato's inequality. Also, some applications to Schrödinger operators coming from the Mathematical-Physics context are given.
 
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Dissertacao_Mestrado.pdf (864.77 Kbytes)
Publishing Date
2015-04-08
 
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