Spectral analysis of a q-difference operator

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...

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Bibliographic Details
Published inJournal of physics. A, Mathematical and theoretical Vol. 43; no. 14; p. 145207
Main Authors Bekker, Miron B, Bohner, Martin J, Herega, Alexander N, Voulov, Hristo
Format Journal Article
LanguageEnglish
Published Bristol IOP Publishing 09.04.2010
IOP
Subjects
Exact sciences and technology
Intervals
Mathematical models
Operators
Physics
Spectra
Second order
Models
Differential operator
Spectral analysis
Singular operator
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Summary: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.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
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ISSN:1751-8121
1751-8113
1751-8121
DOI:10.1088/1751-8113/43/14/145207