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Doctoral Thesis
DOI
10.11606/T.45.2017.tde-28032017-104513
Document
Author
Full name
Luis Fernando Ragognette
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Paulo, 2016
Supervisor
Committee
Cordaro, Paulo Domingos (President)
Barostichi, Rafael Fernando
Hoepfner, Gustavo
Petronilho, Gerson
Zani, Sergio Luis
Title in Portuguese
Operadores ultradiferenciais no estudo de resolubilidade e regularidade Gevrey
Keywords in Portuguese
Funções Gevrey
Operadores ultradiferenciais
Resolubilidade
Abstract in Portuguese
A essência desta tese são resultados e aplicações da teoria de operadores de ordem infinita. A ideia central deste trabalho é um teorema de representação de ultradistribuições a partir de operadores ultradiferenciais agindo em funções Gevrey. Essa representação junto com a regularidade do kernel destes operadores nos permite importar uma dada propriedade válida para funções Gevrey para o contexto de ultradistribuições e vice-versa. Aproveitamos estes teoremas para aprender um pouco mais sobre a resolubilidade local de complexos induzidos por estruturas localmente integráveis. Definimos três conceitos de resolubilidade local destes complexos no ambiente Gevrey e provamos a equivalência entre eles. Para tanto, foi necessário estudar espaços de funções Gevrey com respeito a uma dada estrutura hipo-analítica e investigar quando este novo espaço é isomorfo ao usual. E isto nos permitiu entender melhor a ação dos operadores considerados e o papel por eles desempenhado nesta teoria.
Title in English
Ultradifferential operators in the study of Gevrey solvability and regularity
Keywords in English
Gevrey functions
Solvability
Ultradifferential operators
Abstract in English
The essence of this thesis are results and applications of the theory of infinite order operators. The central idea of this work is a representation theorem of ultradistributions by ultradifferential operators acting on Gevrey functions. This representation together with the regularity of the kernel of these operators allow us to import a given property from Gevrey functions to the ultradistribution context and vice versa. We took advantage of these theorems to learn a little more about the local solvability of the complexes induced by locally integrable structures. We defined three concepts of local solvability of these complexes in the Gevrey environment and we proved that they are equivalent. To do so, it was necessary to study the space of the Gevrey functions with respect to a given hypo-analytic structure and to investigate when this new space is isomorphic to the usual one. And this allowed us to better understand the action of the considered operators and their role in this theory.
 
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teseLuisFRagognette.pdf (763.66 Kbytes)
Publishing Date
2017-07-20
 
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