Jacobi Matrices with Power-like Weights—Grouping in Blocks Approach
✍ Scribed by Jan Janas; Serguei Naboko
- Publisher
- Elsevier Science
- Year
- 1999
- Tongue
- English
- Weight
- 197 KB
- Volume
- 166
- Category
- Article
- ISSN
- 0022-1236
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✦ Synopsis
The paper deals with Jacobi matrices with weights * k given by * k =k : (1+2 k ), where : # ( 1 2 , 1) and lim k 2 k =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.
1999 Academic Press
1. Introduction
Let W be a unilateral weighted shift operator defined in l 2 by We n = 2* n e n+1 , where e n is the canonical basis in l 2 , * n # (0,