A Fourier-RKHS approach for detecting orthogonal Gaussian distributions for stationary processes on homogeneous spaces

TL;DR

This paper introduces a Fourier-RKHS method to identify orthogonal Gaussian distributions in stationary processes on homogeneous spaces, offering a new spectral measure perspective.

Contribution

It presents a novel RKHS-based framework for characterizing Gaussian distribution equivalences in stationary processes on homogeneous spaces.

Findings

Spectral measures characterize Gaussian distribution equivalence.

RKHS approach provides new insights into stationary processes.

Method enhances understanding of Gaussian distributions on homogeneous spaces.

Abstract

Pairs of equivalent Gaussian distributions for centered stationary processes on homogeneous spaces can be characterized in terms of their spectral measures. The purpose of this note is to consider part of the latter characterization from the perspective of a reproducing kernel Hilbert space (RKHS) approach.