On the discrete spectrum of complex banded matrices (original) (raw)

The discrete spectrum of complex banded matrices which are compact perturbations of the standard banded matrix of order ppp 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 ppp-banded matrix with the discrete spectrum having exactly ppp preassigned points on the interval (−2,2)(-2,2)(−2,2) is constructed. The results are applied to the study of the discrete spectrum of asymptotically periodic complex Jacobi matrices.