Infinite-Dimensional Stochastic Transforms and Reproducing Kernel Hilbert space

TL;DR

This paper introduces two new infinite-dimensional transforms connecting Gaussian fields and RKHS, leading to a novel Fourier transform for Gaussian processes that unifies existing infinite-dimensional analysis tools.

Contribution

It constructs two new infinite-dimensional transforms bridging Gaussian fields and RKHS, and develops a new Fourier transform for Gaussian processes, unifying existing analysis tools.

Findings

Development of two infinite-dimensional transforms

Introduction of a new Fourier transform for Gaussian processes

Unification of existing infinite-dimensional analysis tools

Abstract

By way of concrete presentations, we construct two infinite-dimensional transforms at the crossroads of Gaussian fields and reproducing kernel Hilbert spaces (RKHS), thus leading to a new infinite-dimensional Fourier transform in a general setting of Gaussian processes. Our results serve to unify existing tools from infinite-dimensional analysis.