Approximation theory on Riemann surfaces

• Grant number: 22/12756-1
• Support Opportunities: Scholarships abroad - Research Internship - Doctorate (Direct)
• Start date: February 01, 2023
• End date: January 31, 2024
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Guilherme Lima Ferreira da Silva
• Grantee: Victor Julio Alves de Souza
• Supervisor: Andrei Martínez-Finkelshtein
• Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil
• Institution abroad: Baylor University, United States
• Associated to the scholarship: 20/13183-0 - A free boundary problem in potential theory and singularity distribution of solutions to Painlevé equations, BP.DD

Abstract

Padé approximants on the complex plane are generalizations of Taylor Polynomials with countless applications on approximation theory, signal processing, mathematical physics, point processes, among many others. Many results concerning the rate of convergence of such approximants are classical in the literature, and for almost every one of there is the need of understanding an underlying equilibrium problem in potential theory. Recently, Bertola \cite{Bertola1} built up the first steps towards developing a general theory of Padé approximants over compact Riemann surfaces. This project has the goal of pushing forward these recent developments, investigating generalizations of classical results and connections of Padé approximants under the light of such new developments. (AU)