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Abstract

This work deals with a class of Jacobi matrices with power-like weights. The main theme is spectral analysis of matrices with zero diagonal and weights $\lambda_n:=n^{\alpha}(1+{\mit\Delta}_n)$ where $\alpha\in\left(0,1\right] $. Asymptotic formulas for generalized eigenvectors are given and absolute continuity of the matrices considered is proved. The last section is devoted to spectral analysis of Jacobi matrices with $q_n=n+1+(-1)^n$ and $\lambda_n=\sqrt{q_{n-1}q_n}$.