arxiveess.SPcs.ITmath.NA2026-06-26
Matched Generators for the Karhunen--Loève Transform: A Double-Commutator Eigenvalue Theory
The Karhunen--Loève transform (KLT) diagonalizes the covariance of a second-order process and is optimal for mean-square truncation. Which classical transform it reduces to is governed by the symmetry commutant of the covariance: when the kernel commutes with a group action, the…