Judge, Edmund, Naboko, Serguei, Wood, Ian (2016) Eigenvalues for perturbed periodic Jacobi matrices by the Wigner-von Neumann approach. Integral Equations and Operator Theory, 85 (3). pp. 427-450. ISSN 0378-620X. E-ISSN 1420-8989. (doi:10.1007/s00020-016-2302-5) (KAR id:55954)
PDF
Author's Accepted Manuscript
Language: English |
|
Download this file (PDF/363kB) |
![]() |
Request a format suitable for use with assistive technology e.g. a screenreader | |
Official URL: http://dx.doi.org/10.1007/s00020-016-2302-5 |
Abstract
The Wigner-von Neumann method, which has previously been used for perturbing continuous Schrödinger operators, is here applied to their discrete counterparts. In particular, we consider perturbations of arbitrary T-periodic Jacobi matrices. The asymptotic behaviour of the subordinate solutions is investigated, as too are their initial components, together giving a general technique for embedding eigenvalues, ?, into the operator’s absolutely continuous spectrum. Introducing a new rational function, C(?;T), related to the periodic Jacobi matrices, we describe the elements of the a.c. spectrum for which this construction does not work (zeros of C(?;T)); in particular showing that there are only finitely many of them.
Item Type: | Article |
---|---|
DOI/Identification number: | 10.1007/s00020-016-2302-5 |
Uncontrolled keywords: | Spectral theory, Periodic Jacobi operators, Wigner-von Neumann potential, Subordinate solutions |
Subjects: | Q Science > QA Mathematics (inc Computing science) > QA299 Analysis, Calculus |
Divisions: | Divisions > Division of Computing, Engineering and Mathematical Sciences > School of Mathematics, Statistics and Actuarial Science |
Depositing User: | Ian Wood |
Date Deposited: | 15 Jun 2016 14:28 UTC |
Last Modified: | 10 Dec 2022 02:04 UTC |
Resource URI: | https://kar.kent.ac.uk/id/eprint/55954 (The current URI for this page, for reference purposes) |
- Link to SensusAccess
- Export to:
- RefWorks
- EPrints3 XML
- BibTeX
- CSV
- Depositors only (login required):