On the discrete spectrum of complex banded matrices

Abstract

The discrete spectrum of complex banded matrices which are compact perturbations of the standard banded matrix of order $p$ is under consideration. The rate of stabilization for the matrix entries sharp in the sense of order which provides finiteness of the discrete spectrum is found. The $p$-banded matrix with the discrete spectrum having exactly $p$ preassigned points on the interval $(-2,2)$ is constructed. The results are applied to the study of the discrete spectrum of asymptotically periodic complex Jacobi matrices.

LaTeX, 22 pages

References in corpus (3)

• On the discrete spectrum of complex banded matrices
• On the spectrum of Jacobi operators with quasi-periodic algebro-geometric coefficients
• On location of discrete spectrum for complex Jacobi matrices

Cited by in corpus (7)

• On the discrete spectrum of complex banded matrices
• Embedded eigenvalues for perturbed periodic Jacobi operators using a geometric approach
• Number of eigenvalues for a class of non-selfadjoint Schrödinger operators
• Counting eigenvalues of Schrödinger operator with complex fast decreasing potential
• Spectral properties of some complex Jacobi matrices
• On the number of zeros of functions in analytic quasianalytic classes
• Lieb--Thirring bounds for complex Jacobi matrices