Spectral properties of a q-Sturm–Liouville Operator

Brown, Brian Malcolm ORCID: https://orcid.org/0000-0002-2871-6591, Christiansen, Jacob S. and Schmidt, Karl Michael ORCID: https://orcid.org/0000-0002-0227-3024 2009. Spectral properties of a q-Sturm–Liouville Operator. Communications in Mathematical Physics 287 (1) , pp. 259-274. 10.1007/s00220-008-0623-1

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Abstract

We study the spectral properties of a class of Sturm-Liouville type operators on the real line where the derivatives are replaced by a q-difference operator which has been introduced in the context of orthogonal polynomials. Using the relation of this operator to a direct integral of doubly-infinite Jacobi matrices, we construct examples for isolated pure point, dense pure point, purely absolutely continuous and purely singular continuous spectrum. It is also shown that the last two spectral types are generic for analytic coefficients and for a class of positive, uniformly continuous coefficients, respectively.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Mathematics Computer Science & Informatics
Subjects:	Q Science > QA Mathematics
Publisher:	Springer
ISSN:	0010-3616
Last Modified:	18 Oct 2022 13:15
URI:	https://orca.cardiff.ac.uk/id/eprint/13233

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