Basic functional analysis and introduction to distribution theory

• Grant number: 18/09547-6
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: October 01, 2018
• End date: September 30, 2019
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Marcos Tadeu de Oliveira Pimenta
• Grantee: Wendy Fernanda de Almeida
• 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 from Functional Analysis, as well as Weak Topologies and Distribution Theory. In a first moment, the student will do a brief revision of several topics on Metric Spaces, what will be useful in the study of deeper topics. We pretend study the normed vectorial spaces, topologic language and Baire Theorem. The Hahn-Banach Theorem also will be of interest, since it is a central result in Functional Analysis. We aim also to study in an introductory level the Distribution Theory.