New characterizations of reproducing kernel Hilbert spaces and applications to metric geometry

TL;DR

This paper introduces two new global and algorithmic methods for constructing reproducing kernel Hilbert spaces, extends the framework to measurable kernels, and explores applications in stochastic analysis and metric geometry.

Contribution

It provides novel global and algorithmic constructions of RKHS, generalizes the setting to measurable kernels, and offers new examples and applications.

Findings

New global and algorithmic RKHS constructions

Extension to measurable positive definite kernels

Applications to stochastic analysis and metric geometry

Abstract

We give two new global and algorithmic constructions of the reproducing kernel Hilbert space associated to a positive definite kernel. We further present ageneral positive definite kernel setting using bilinear forms, and we provide new examples. Our results cover the case of measurable positive definite kernels, and we give applications to both stochastic analysisand metric geometry and provide a number of examples.