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Master's Dissertation
DOI
10.11606/D.55.2018.tde-25102018-112308
Document
Author
Full name
Hugo Cattarucci Botós
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Carlos, 2018
Supervisor
Committee
Zani, Sergio Luis (President)
Bergamasco, Adalberto Panobianco
Medeira, Cléber de
Santos Filho, José Ruidival Soares dos
Title in Portuguese
Propriedades globais de uma classe de complexos diferenciais
Keywords in Portuguese
Análise de Fourier.
Condições diofantinas
Hipoeliticidade global
Resolubilidade global
Vetores de Liouville
Abstract in Portuguese
Considere a variedade Tn x S1 com coordenadas (t;x) e considere uma 1-forma diferencial fechada e real a(t) em Tn. Neste trabalho consideramos o operador Lpa = dt +a(t) Λ ∂x de D'p em D'p+1, onde D'p é o espaço das p-correntes da forma u = ∑ Ι I Ι = puI (t, x)dtI. O operador acima define um complexo de cocadeia formado pelos espaços vetoriais D'p e pelos homomorfismos lineares Lpa : D'p → D'p+1. Definiremos o que significa resolubilidade global no complexo acima e caracterizaremos para quais 1-formas a o complexo é globalmente resolúvel. Faremos o mesmo com respeito a hipoeliticidade global no primeiro nível do complexo.
Title in English
Global properties of a class of differential complexes
Keywords in English
Diophantine conditions
Fourier analysis.
Global hypoellipticity
Global solvability
Liouville vector
Abstract in English
Consider the manifold Tn x S1 with coordinates (t;x) and let a(t) be a real and closed differential 1-form on Tn. In this work we consider the operator Lpsub>a = dt +a(t) Λ ∂x de D'p from D'p to D'p+1, where D'p is the space of all p-currents u = ∑ Ι I Ι = puI (t, x)dtI . The above operator defines a cochain complex consisting of the vector spaces D'p and of the linear maps Lpa : D'p → D'p+1. We define what global solvability means for the above complex and characterize for which 1-forms a the complex is globally solvable. We will do the same with respect to global hypoellipticity on the first level of the complex.
 
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Publishing Date
2018-10-25
 
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