Center for Advanced Intelligence Project

Speaker: Dr. Jean Carlo Guella (UNIVERSIDADE DE SÃO PAULO)

Title: Positive definite kernels and Schoenberg’s legacy

Abstract:
Positive definite kernels have become a mathematical concept that permeates several areas of mathematics in both theoretical and applied aspects such as mathematical analysis, probability theory,
approximation theory, numerical analysis, machine learning, and spatial statistics. This is mainly due to the simplicity and versatility of the concept. A leading figure in this topic was I.J. Schoenberg who obtained several outstanding results in the theory, most of them in the late thirties and early forties. Among them, there is a characterization for the continuous positive definite kernels on a real sphere that is invariant by rotations (usually called isotropic) and a characterization for the continuous positive definite kernels on a Euclidean space that are invariant by rotations and translations (usually called radial). In this talk, I will present some of Schoenberg’s results on positive definite kernels along with some recent developments on the topic.