On the discrete spectrum of complex banded matrices

Details On the discrete spectrum of complex banded matrices On the discrete spectrum of complex banded matrices

2005-11-22

arxiv.org/abs/math/0511566v1

Mathematics

Spectral Theory

LaTeX, 22 pages

Scientific paper

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.

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