About essential spectra of unbounded Jacobi matrices
Grzegorz \'Swiderski, Bartosz Trojan
TL;DR
This paper investigates the spectral characteristics of unbounded Jacobi matrices with periodic or blended entries, using asymptotic analysis to determine self-adjointness and describe the essential spectrum.
Contribution
It provides a comprehensive analysis of the essential spectrum for a class of unbounded Jacobi matrices with novel asymptotic methods.
Findings
Identifies conditions for self-adjointness of the operators.
Characterizes regions with no accumulation points in the point spectrum.
Provides a complete description of the essential spectrum.
Abstract
We study spectral properties of unbounded Jacobi matrices with periodically modulated or blended entries. Our approach is based on uniform asymptotic analysis of generalized eigenvectors. We determine when the studied operators are self-adjoint. We identify regions where the point spectrum has no accumulation points. This allows us to completely describe the essential spectrum of these operators.
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