Spectral averaging techniques for Jacobi matrices with matrix entries

TL;DR

This paper introduces spectral averaging methods for Jacobi matrices with matrix entries, providing explicit formulas for the averaged spectral measure and exploring averaging over boundary conditions and coupling constants.

Contribution

It presents new spectral averaging formulas for matrix-valued Jacobi operators, enhancing tools for spectral analysis of these complex matrices.

Findings

Explicit formulas for averaged spectral measures

New spectral averaging techniques over boundary conditions

Spectral averaging over coupling constants

Abstract

A Jacobi matrix with matrix entries is a self-adjoint block tridiagonal matrix with invertible blocks on the off-diagonals. Averaging over boundary conditions leads to explicit formulas for the averaged spectral measure which can potentially be useful for spectral analysis. Furthermore another variant of spectral averaging over coupling constants for these operators is presented.