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Master's Dissertation
DOI
10.11606/D.45.2008.tde-16102008-174340
Document
Author
Full name
Rodrigo Ferraz de Andrade
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Paulo, 2008
Supervisor
Committee
Melo, Severino Toscano do Rego (President)
Santos Filho, José Ruidival Soares dos
Tausk, Daniel Victor
Title in Portuguese
O teorema do índice para o círculo
Keywords in Portuguese
Álgebra de Comparação
Espaço de Gelfand
Teoria do índice de Fredholm
Abstract in Portuguese
Estudamos a álgebra de comparação do círculo, descrevemos o espaço de Gelfand do seu quociente pelos compactos e damos uma fórmula para o índice dos seus operadores de Fredholm. Depois generalizamos o resultado para as matrizes com elementos na álgebra de comparação e damos uma aplicação para operadores diferenciais no círculo.
Title in English
The index theorem for the circle
Keywords in English
Comparison Algebra
Gelfand Space
Theory of the Fredholm index
Abstract in English
We study the comparison algebra on the circle, we describe the Gelfand space of its quotient by the compacts and we give a formula to compute the index of its Fredholm operators. After that, we generalize the result to the matrices with entries in the comparison algebra and give an application to differential opperators in the circle.
 
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Publishing Date
2008-11-12
 
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