Introduction to the functional analysis

• Grant number: 21/12723-3
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: February 01, 2022
• End date: January 31, 2023
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Marcos Tadeu de Oliveira Pimenta
• Grantee: Mariele Vaz Quiraldello
• Host Institution: Faculdade de Ciências e Tecnologia (FCT). Universidade Estadual Paulista (UNESP). Campus de Presidente Prudente. Presidente Prudente , SP, Brazil

Abstract

In this project, we propose an introductory study of the main results of Functional Analysis. At first, the student will study several topics of Metric Spaces, which will serve as a subsidy to be able to progress in the study of Functional Analysis topics. It is intended to study the normed vector spaces, going through topological notions that allow enunciating and proving Baire's Theorem and finally studying its consequences. The Hahn-Banach Theorem will also be of interest in this project, given its importance in demonstrating several Functional Analysis results. Finally, we intend to study the Lebesgue spaces Lp(©) and their main properties.(AU)