Study and Generalization of the Weierstrass Approximation Theorem and Stone's Generalization.

• Grant number: 24/14437-6
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: November 01, 2024
• End date: October 31, 2025
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Stefano Nardulli
• Grantee: Athaide Belo da Silva Santos
• Host Institution: Centro de Matemática, Computação e Cognição (CMCC). Universidade Federal do ABC (UFABC). Ministério da Educação (Brasil). Santo André , SP, Brazil
• Associated research grant: 21/05256-0 - Geometric variational problems: existence, regularity and geometrical characterization of the solutions, AP.JP

Abstract

The objective of this project is to study the Weierstrass Approximation Theorem, which guarantees that any continuous function defined on a closed interval can be approximated by polynomials with desired precision. The project will also address the generalization of the theorem by Marshall Stone, which extends the concepts to function algebras. The study will explore proofs, practical examples, and implications of these theories, as well as applications in various areas of mathematics and computational science.