On the Discrete Spectrum of Complex Banded Matrices - Golinskii, L.; Kudryavtsev, M. (Журнал математичної фізики, аналізу, геометрії, 2006)
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.