A Fock space approach to the theory of strictly positive kernels

TL;DR

This paper introduces a novel Fock space-based method for analyzing strictly positive kernels, providing new proofs and examples, and enhancing understanding of kernel approximation properties.

Contribution

It presents a new Fock space approach to the theory of strictly positive kernels, including new proofs and diverse examples.

Findings

New Fock space framework for positive kernels

Examples of strictly positive kernels provided

Alternative proof of universal approximation theorem for Gauss kernel

Abstract

In this paper, we give a new approach to the theory of strictly positive kernels. Our method is based on the structure of Fock spaces. As its applications, various examples of strictly positive kernels are given. Moreover, we give a new proof of the universal approximation theorem for the Gauss kernel.