Infinite-dimensional Christoffel-Darboux polynomial kernels on Hilbert spaces

TL;DR

This paper extends the Christoffel-Darboux polynomial kernel to infinite-dimensional Hilbert spaces, adapting its finite-dimensional formulation to a broader mathematical context.

Contribution

It introduces a novel infinite-dimensional version of the Christoffel-Darboux polynomial kernel, expanding its applicability in functional analysis and machine learning.

Findings

Successfully generalizes the kernel to infinite dimensions

Maintains key properties of the finite-dimensional kernel

Provides a foundation for future applications in Hilbert spaces

Abstract

In these notes, the Christoffel-Darboux polynomial kernel is extended to infinite-dimensional Hilbert spaces, following as closely as possible its original finite-dimensional treatment.