Riez basis and non-harmonic Fourier series

• Grant number: 21/14684-5
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: April 01, 2022
• End date: March 31, 2023
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Alexandre Kawano
• Grantee: Lucas Nunes Fernandes Teles
• Host Institution: Escola Politécnica (EP). Universidade de São Paulo (USP). São Paulo , SP, Brazil

Abstract

In this research proposal, we aim to prove a theorem due to Paley\& Wiener on bases in Banach spaces and its applications in non-harmonic Fourier series. In the process, several ideas about Banach spaces, Hilbert spaces, and the representation of functions through non-harmonic Fourier series are visited. The results have applications in the analysis of inverse problems.(AU)