Eigenfunction expansion in the singular case for \(q\)-Sturm-Liouville operators. (English) Zbl 1463.39008
Summary: In this work, we prove the existence of a spectral function for singular \(q\)-Sturm-Liouville operator. Further, we establish a Parseval equality and expansion formula in eigenfunctions by terms of the spectral function.
MSC:
| 39A13 | Difference equations, scaling (\(q\)-differences) |
| 39A12 | Discrete version of topics in analysis |
| 39A70 | Difference operators |
| 05A30 | \(q\)-calculus and related topics |
| 34B24 | Sturm-Liouville theory |
| 34L10 | Eigenfunctions, eigenfunction expansions, completeness of eigenfunctions of ordinary differential operators |
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