Spectral theory of a class of Block Jacobi matrices and applications

TL;DR

This paper develops a spectral analysis framework for a class of block Jacobi operators using Mourre's conjugate operator method, with applications to various difference operators and wave propagators.

Contribution

It introduces a novel spectral analysis approach for block Jacobi matrices and applies it to diverse operators like periodic scalar Jacobi and higher-order difference operators.

Findings

Spectral properties of block Jacobi matrices are characterized.

Applications include analysis of wave propagators and higher-order difference operators.

The method provides new insights into the spectral behavior of these operators.

Abstract

We develop a spectral analysis of a class of block Jacobi operators based on the conjugate operator method of Mourre. We give several applications including scalar Jacobi operators with periodic coefficients, a class of difference operators on cylindrical domains such as discrete wave propagators, and certain fourth-order difference operators.