An expansion theorem for \(q\)-Sturm-Liouville operators on the whole line. (English) Zbl 1424.39018
Summary: In this work, we establish a Parseval equality and an expansion formula in eigenfunctions for a singular \(q\)-Sturm-Liouville operator on the whole line.
MSC:
| 39A13 | Difference equations, scaling (\(q\)-differences) |
| 33D05 | \(q\)-gamma functions, \(q\)-beta functions and integrals |
| 34L10 | Eigenfunctions, eigenfunction expansions, completeness of eigenfunctions of ordinary differential operators |
| 34L40 | Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) |
Keywords:
\(q\)-Sturm-Liouville operator; singular point; Parseval equality; spectral function; eigenfunction expansionReferences:
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