TY - JOUR

T1 - Jacobi Matrices with Power-like Weights - Grouping in Blocks Approach

AU - Janas, Jan

AU - Naboko, Serguei

PY - 1999/8/20

Y1 - 1999/8/20

N2 - The paper deals with Jacobi matrices with weights λk given by λk=kα(1+Δk), where α∈(12, 1) and limkΔk=0. The main question studied here concerns when the spectrum of the operator J defined by the Jacobi matrix has absolutely continuous component covering the real line. A sufficient condition is given for a positive answer to the above question. The method used in the paper is based on a detailed analysis of generalized eigenvectors of J. In turn this analysis relies on the so-called grouping in blocks approach to a large product of the transfer matrices associated to J.

AB - The paper deals with Jacobi matrices with weights λk given by λk=kα(1+Δk), where α∈(12, 1) and limkΔk=0. The main question studied here concerns when the spectrum of the operator J defined by the Jacobi matrix has absolutely continuous component covering the real line. A sufficient condition is given for a positive answer to the above question. The method used in the paper is based on a detailed analysis of generalized eigenvectors of J. In turn this analysis relies on the so-called grouping in blocks approach to a large product of the transfer matrices associated to J.

UR - http://www.scopus.com/inward/record.url?scp=0001038223&partnerID=8YFLogxK

U2 - 10.1006/jfan.1999.3434

DO - 10.1006/jfan.1999.3434

M3 - Article

AN - SCOPUS:0001038223

VL - 166

SP - 218

EP - 243

JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

SN - 0022-1236

IS - 2

ER -