On location of discrete spectrum for complex Jacobi matrices

TL;DR

This paper investigates the spectral properties of complex Jacobi matrices, identifying conditions under which they lack discrete spectra, especially when they are compact perturbations of the discrete Laplacian.

Contribution

It provides new criteria for the absence of discrete spectrum in complex Jacobi matrices that are compact perturbations of the discrete Laplacian.

Findings

Identified spectrum inclusion regions for these matrices.

Established sufficient conditions for no discrete spectrum.

Enhanced understanding of spectral stability under perturbations.

Abstract

We study spectrum inclusion regions for complex Jacobi matrices which are compact perturbations of the discrete laplacian. The condition sufficient for the lack of discrete spectrum for such matrices is given.