An FBI characterization for Gevrey vectors on hypo-analytic structures and propagation of Gevrey singularities

• Ano de defesa: 2020
• Autor(a) principal: Rodrigues, Nicholas Braun
• Tipo de documento: Tese
• Tipo de acesso: Acesso aberto
• Idioma: eng
• Instituição de defesa: Biblioteca Digitais de Teses e Dissertações da USP
• Palavras-chave em Português: Estruturas hipo-analíticas; FBI transform; Gevrey vectors; Hypo-analytic structures; Propagação de singularidades; Propagation of singularities; Transformada FBI; Vetores Gevrey
• Link de acesso: https://www.teses.usp.br/teses/disponiveis/45/45132/tde-30062020-114522/

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.