On limit sets for the discrete spectrum of complex Jacobi matrices

Details On limit sets for the discrete spectrum of complex Jacobi matrices On limit sets for the discrete spectrum of complex Jacobi matrices

2005-02-25

arxiv.org/abs/math/0502544v1

Mathematics

Spectral Theory

LaTeX, 24 pages

Scientific paper

The discrete spectrum of complex Jacobi matrices that are compact perturbations of the discrete laplacian is under consideration. The rate of stabilization for the the matrix entries which provides finiteness of the discrete spectrum and is sharp in the sense of order is found. The Jacobi matrix with the discrete spectrum having a single limit point is constructed. The results can be viewed as the discrete analogs of the well known theorems by B.S. Pavlov about Schr\"odinger operators on the half line with a complex potential.

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