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Jacobi Matrices with Power-like Weights—Grouping in Blocks Approach by Jan Janas; Serguei Naboko is a Mathematics article available to read on EtoBox.
What is Jacobi Matrices with Power-like Weights—Grouping in Blocks Approach about?
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,
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- Author
- Jan Janas; Serguei Naboko
- Publisher
- Elsevier Science; Elsevier ; Elsevier Inc.; Elsevier BV (ISSN 0022-1236)
- Published
- 1999
- Language
- EN
- Field
- Mathematics (Physical Sciences)