Os espaços L^q-Gevrey globais

• Processo: 16/00352-2
• Modalidade de apoio: Auxílio à Pesquisa - Pesquisador Visitante - Internacional
• Data de Início da vigência: 06 de março de 2016
• Data de Término da vigência: 15 de março de 2016
• Área do conhecimento: Ciências Exatas e da Terra - Matemática - Análise
• Pesquisador responsável: Gustavo Hoepfner
• Beneficiário: Gustavo Hoepfner
• Pesquisador visitante: Andrew Seth Raich
• Instituição do Pesquisador Visitante: University of Arkansas, Estados Unidos
• Instituição Sede: Centro de Ciências Exatas e de Tecnologia (CCET). Universidade Federal de São Carlos (UFSCAR). São Carlos , SP, Brasil
• Vinculado ao auxílio: 12/03168-7 - Teoria geométrica de EDP e várias variáveis complexas, AP.TEM
• Assunto(s): Análise de Fourier Análise funcional Intercâmbio de pesquisadores
• Palavra(s)-Chave do Pesquisador: Análise microlocal | Espaços Gevrey | Transformada FBI | Análise de Fourier, Análise Funcional

Resumo

The goal of this research project is to continue out investigation on a class of $C^\infty$ functions whose derivatives satisfy quantitative size estimates. The estimates, called {global $L^q$ Gevrey estimates}, first arose in the work of Boggess and Raich \cite{BoRa13h} when they investigated how to capture a particular type of exponential decay through estimates on the Fourier transform. In this project, we propose to refine the notion of global $L^q$-Gevrey functions and include a discussion of the function theory as well as the relationship to Gevrey classes and known function spaces. Additionally, we present explicit examples of global $L^q$-Gevrey functions and ways to generate new global $L^q$-Gevrey functions from old ones. We also want to investigate some applications: The first is solving a Carleman-type problem for constructing functions whose derivatives are a given sequence of global $L^q$-Gevrey functions. The other two applications concern extensions of a given global $L^q$-Gevrey function: the first is constructing an almost analytic extension, and the second is building an approximate solution to a first-order complex vector field whose coefficients are global $L^q$-Gevrey functions. (AU)