Absolute continuity for Jacobi matrices with power-like weights

Wojciech Motyka

Wojciech Motyka

Colloquium Mathematicae, Tome 107 (2007), p. 179-190 / Harvested from The Polish Digital Mathematics Library

Résumé

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 $λ ₙ : = n^{α} (1 + Δ ₙ)$ where α ∈ (0,1]. 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 qₙ = n + 1 + (-1)ⁿ and $λ ₙ = \sqrt (q_{n - 1} q ₙ)$ .

Publié le : 2007-01-01

Zbl 1119.47028

EUDML-ID : urn:eudml:doc:284009

@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm107-2-2,
     author = {Wojciech Motyka},
     title = {Absolute continuity for Jacobi matrices with power-like weights},
     journal = {Colloquium Mathematicae},
     volume = {107},
     year = {2007},
     pages = {179-190},
     zbl = {1119.47028},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm107-2-2}
}

Wojciech Motyka. Absolute continuity for Jacobi matrices with power-like weights. Colloquium Mathematicae, Tome 107 (2007) pp. 179-190. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm107-2-2/