Geodesic
Absolute continuity for Jacobi matrices with power-like weights
Wojciech Motyka1
1 Institute of Mathematics Polish Academy of Sciences Św. Tomasza 30 31-027 Kraków, Poland
Colloquium Mathematicum, Tome 107 (2007) no. 2, pp. 179-190 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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 $\lambda_n=\sqrt{q_{n-1}q_n}$.
DOI : 10.4064/cm107-2-2
Keywords: work deals class jacobi matrices power like weights main theme spectral analysis matrices zero diagonal weights lambda alpha mit delta where alpha right asymptotic formulas generalized eigenvectors given absolute continuity matrices considered proved section devoted spectral analysis jacobi matrices lambda sqrt n

Wojciech Motyka 1

1 Institute of Mathematics Polish Academy of Sciences Św. Tomasza 30 31-027 Kraków, Poland 
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Wojciech Motyka. Absolute continuity for Jacobi matrices
with power-like weights. Colloquium Mathematicum, Tome 107 (2007) no. 2, pp. 179-190. doi: 10.4064/cm107-2-2

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