On the Discrete Spectrum of Complex Banded Matrices

Анотація

The discrete spectrum of complex banded matrices that 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 limit points on the interval (-2,2) is constructed. The results are applied to study the discrete spectrum of asymptotically periodic Jacobi matrices.

Mathematics Subject Classification: 47B36, 47A10.