Introducción a la teoría de los espacios de Hilbert de núcleos reproductores y algunas aplicaciones

Abstract

This work explores the foundations of Reproducing Kernel Hilbert Spaces and their applications. The first part, consisting of the three initial chapters, is dedicated to the study of the fundamental properties and characterizations of these spaces, including their connection with integral operators. The second part, consisting of chapters 4 and 5, is devoted to the applications of Reproducing Kernel Hilbert Spaces (RKHS). In chapter 4, we examine how RKHS relate to Probability Theory as well as to stochastic processes. Finally, in chapter 5 we explore how RKHS are applied in statistics and machine learning, leading to the generalization of learning algorithms to nonlinear problems through the use of the kernel trick.