An approach to functional analysis by real functions, integral equations and Hilbert spaces

• Grant number: 22/06815-5
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: August 01, 2022
• End date: July 31, 2023
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Thaís Jordão
• Grantee: Vinícius Trujillo Mazza
• Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil

Abstract

This project is based on exploring fundamental concepts of analysis, in particular the study of functions spaces and operators, from the view of real functions. The objective is to develop with the student basic ideas of functional analysis in the context of real analysis and containing elements of Approximation Theory. This approach, directed to the supervisor's specialty, isn't covered by any regular subject and it would be an opportunity for the student to know more about the researcher's area. For this purpose the book "Functional Analysis" by Riesz & Nagy (1956), which offers a great disposition of those concepts and requires few prerequisites (a subject of Analysis), will be adopted as the main reference, aiming at the understanding of Mercer's Theorem.(AU)