Spectral Analysis of a Q-difference Operator

Author

Miron B. Bekker
Martin Bohner, Missouri University of Science and TechnologyFollow
Alexander N. Herega
Hristo Voulov

Editor(s)

Batchelor, M. T.

Abstract

For a number q bigger than 1, we consider a q-difference version of a second-order singular differential operator which depends on a real parameter. We give three exact parameter intervals in which the operator is semibounded from above, not semibounded, and semibounded from below, respectively. We also provide two exact parameter sets in which the operator is symmetric and self-adjoint, respectively. Our model exhibits a more complex behavior than in the classical continuous case but reduces to it when q approaches 1.

Recommended Citation

M. B. Bekker et al., "Spectral Analysis of a Q-difference Operator," Journal of Physics A: Mathematical and Theoretical, Institute of Physics - IOP Publishing, Jan 2010.

The definitive version is available at https://doi.org/10.1088/1751-8113/43/14/145207

Department(s)

Mathematics and Statistics

International Standard Serial Number (ISSN)

1751-8113

Document Type

Article - Journal

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 2010 Institute of Physics - IOP Publishing, All rights reserved.

Publication Date

01 Jan 2010