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Eigenvalues for perturbed periodic Jacobi matrices by the Wigner-von Neumann approach

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)

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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: Faculties > Sciences > School of Mathematics Statistics and Actuarial Science
Depositing User: Ian Wood
Date Deposited: 15 Jun 2016 14:28 UTC
Last Modified: 29 May 2019 17:29 UTC
Resource URI: https://kar.kent.ac.uk/id/eprint/55954 (The current URI for this page, for reference purposes)
Wood, Ian: https://orcid.org/0000-0001-7181-7075
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