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Master's Dissertation
Document
Author
Full name
João Pedro Cardoso da Silva de Vasconcellos
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Carlos, 2024
Supervisor
Committee
Araujo, Gabriel Cueva Candido Soares de (President)
Ferra, Igor Ambo
Kirilov, Alexandre
Zani, Sergio Luis
Title in Portuguese
Existência e regularidade de soluções de certas EDPs lineares em espaços de funções ultradiferenciáveis
Keywords in Portuguese
Funções ultradiferenciáveis
Hipoeliticidade
Resolubilidade
Séries de Fourier
Abstract in Portuguese
Este trabalho trata da existência e regularidade de soluções globais de equações diferenciais parciais de primeira ordem, definidas no toro n-dimensional Tn, Tn = Rn / (2πZn), no contexto de espaços de funções ultradiferenciáveis de tipo Beurling e tipo Roumieu. Apresentamos a caracterização de tais espaços via séries de Fourier. Sob certas condições, obtemos uma forma normal para as equações. Condições diofantinas surgem naturalmente neste trabalho.
Title in English
Existence and regularity of solutions of certain linear PDEs in spaces of ultradifferentiable functions.
Keywords in English
Fourier Series
Hypoellipticity
Solvability
Ultradifferentiable functions
Abstract in English
We study the existence and regularity of global solutions of first order partial differential equations, defined on n-dimensional torus Tn, Tn = Rn / (2πZn), in context of ultradifferentiable function spaces of Beurling type and Roumieu type. We present characterization of such spaces by Fourier series. Under certain condition, we obtain a normal form of our equations. Diophantine conditions appears naturally in this work. Another application of this theory is the study of solvability in the context Beurling and Roumieu ultradiferentiable classes to the operator mentioned above.
 
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Publishing Date
2024-06-19
 
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