Spectral estimates for 2D periodic Jacobi operators

TL;DR

This paper provides estimates for the Lebesgue measure of the spectrum and the edges of spectral bands of 2D periodic Jacobi operators, advancing understanding of their spectral properties.

Contribution

It introduces new bounds on the spectrum measure and spectral band edges for 2D periodic Jacobi operators, which were not previously established.

Findings

Estimate of the Lebesgue measure of the spectrum

Bounds on the edges of spectral bands

Improved spectral analysis techniques

Abstract

For 2D periodic Jacobi operators we obtain the estimate of the Lebesgue measure of the spectrum and estimates of edges of spectral bands.