On limit sets for the discrete spectrum of complex Jacobi matrices

2005/02/25 by Iryna Egorova, I. Egorova, Egorova, I. +3
Mathematics · #47A55 #47B36 #FOS: Mathematics #Holomorphic and Operator Theory #Mathematical functions and polynomials #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics #math.SP #msc:47A55 #msc:47B36

paper · pdf · doi:10.48550/arxiv.math/0502544

LaTeX, 24 pages

arxiv created 2005/02/25 · openalex publication_date 2005/02/25 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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 Schrödinger operators on the half line with a complex potential.

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