Miron B Bekker et al 2010 J. Phys. A: Math. Theor. 43 145207 doi:10.1088/1751-8113/43/14/145207
Spectral analysis of a q-difference operator
Miron B Bekker1, Martin J Bohner2, Alexander N Herega3 and Hristo Voulov1
Show affiliationsFor 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.
- PACS
- MSC
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39A70 Difference operators (See also 47B39)
47B39 Difference operators (See also 39A70)
39A13 Difference equations, scaling (q-differences) (See also 33Dxx)
- Subjects
- Dates
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Issue 14 (9 April 2010)
Received 19 November 2009, in final form 22 February 2010
Published 18 March 2010
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Spectral analysis of a q-difference operator
Miron B Bekker et al 2010 J. Phys. A: Math. Theor. 43 145207
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