Published April 2009
| public
Journal Article
Spectral properties of a q-Sturm–Liouville operator
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.
Additional Information
© Springer 2009. 8 February 2008. Accepted: 29 April 2008. Published online: 20 September 2008. This work was supported by EPSRC grant EP/D03096X/1.Additional details
- Eprint ID
- 14971
- DOI
- 10.1007/s00220-008-0623-1
- Resolver ID
- CaltechAUTHORS:20090811-142354070
- EP/D03096X/1
- Engineering and Physical Sciences Research Council (EPSRC)
- Created
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2009-08-11Created from EPrint's datestamp field
- Updated
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2021-11-08Created from EPrint's last_modified field