Reproducing Kernel Hilbert Spaces of Spherical Functions

• Grant number: 23/16568-8
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: March 01, 2024
• End date: February 28, 2025
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Thaís Jordão
• Grantee: Victor de Angeli Dalarmi
• 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 Functional Analysis and Advanced Calculus, through the concept of reproducing Hilbert spaces and functions defined on the unit sphere of Euclidean space, respectively. The objective is to develop the necessary mathematical background to understand the working environment involved in the search for estimates of epsilon-entropy of Kolmogorov or, equivalently, covering numbers associated with Reproducing Hilbert Spaces.