On Limit Sets for the Discrete Spectrum of Complex Jacobi Matrices

The discrete spectrum of complex Jacobi matrices that are compact perturbations of the discrete laplacian 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 Jacobi matrix with the discrete spectrum having the only limit point is constructed. The results can be viewed as the discrete analogs of the well known theorems by B.S. Pavlov about Schrödinger operators on the half line with a complex potential. Bibliography : 26 references.