Doctoral Thesis
DOI
https://doi.org/10.11606/T.45.2020.tde-30062020-114522
Document
Author
Full name
Nicholas Braun Rodrigues
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Paulo, 2020
Supervisor
Committee
Cordaro, Paulo Domingos (President)
Hoepfner, Gustavo
Hounie, Jorge Guillermo
Petronilho, Gerson
Silva, Paulo Leandro Dattori da
Title in English
An FBI characterization for Gevrey vectors on hypo-analytic structures and propagation of Gevrey singularities
Keywords in English
FBI transform
Gevrey vectors
Hypo-analytic structures
Propagation of singularities
Abstract in English
In this work, we begin by studying the basic structure of Gevrey vectors on hypo-analytic structures, and we compare some basic properties of hypo-analytic functions and Gevrey vectors. Then we prove a FBI characterization for Gevrey vectors, and we point out the main role of the real structure bundle, in contrast to the characterization of hypo-analytic functions. We finish this work with an application, of the FBI characterization, for the propagation of singularities for solutions of the non-homogeneous system equations, associated with a real-analytic hypo-analytic structure of tube type.
Title in Portuguese
Caracterização de vetores Gevrey pela transformada FBI em estruturas hipo-analÃticas e propagação de singularidades Gevrey
Keywords in Portuguese
Estruturas hipo-analÃticas
Propagação de singularidades
Transformada FBI
Vetores Gevrey
Abstract in Portuguese
Neste trabalho exploramos a teoria dos vetores Gevrey em estruturas hipo-analÃticas e mostramos as principais diferenças entre funções hipo-analiticas e vetores Gevrey. Em seguida provamos uma caracterização via transformada FBI para vetores Gevrey e destacamos o papel principal do fibrado estrutural real nesse teorema, em contraste com a caracterização de funções hipo-analÃticas. ConcluÃmos este trabalho com uma aplicação na propagação de singularidades para soluções do sistema de equações não homogêneas, associado à uma estrutura hipo-analÃtica, analÃtica real e do tipo tubo.
WARNING - Viewing this document is conditioned on your acceptance of the following terms of use:
This document is only for private use for research and teaching activities. Reproduction for commercial use is forbidden. This rights cover the whole data about this document as well as its contents. Any uses or copies of this document in whole or in part must include the author's name.
Publishing Date
2021-01-20