Absolute continuity for Jacobi matrices with power-like weights

Wojciech Motyka. "Absolute continuity for Jacobi matrices with power-like weights." Colloquium Mathematicae 107.2 (2007): 179-190. <http://eudml.org/doc/284009>.

@article{WojciechMotyka2007,
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 $λₙ: = n^\{α\}(1 + Δₙ)$ 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 $λₙ = √(q_\{n-1\}qₙ)$.},
author = {Wojciech Motyka},
journal = {Colloquium Mathematicae},
keywords = {Jacobi matrices; asymptotic of solutions; spectral analysis; absolutely continuous spectrum; subordinacy theory; transfer matrices},
language = {eng},
number = {2},
pages = {179-190},
title = {Absolute continuity for Jacobi matrices with power-like weights},
url = {http://eudml.org/doc/284009},
volume = {107},
year = {2007},
}

TY - JOUR
AU - Wojciech Motyka
TI - Absolute continuity for Jacobi matrices with power-like weights
JO - Colloquium Mathematicae
PY - 2007
VL - 107
IS - 2
SP - 179
EP - 190
AB - 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 $λₙ: = n^{α}(1 + Δₙ)$ 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 $λₙ = √(q_{n-1}qₙ)$.
LA - eng
KW - Jacobi matrices; asymptotic of solutions; spectral analysis; absolutely continuous spectrum; subordinacy theory; transfer matrices
UR - http://eudml.org/doc/284009
ER -