An expansion theorem for q -Sturm-Liouville operators on the whole line

DOI10.3906/mat-1705-22zbMath1424.39018OpenAlexW2801671533MaRDI QIDQ4634223

Hüseyin Tuna, Bilender P. Allahverdiev

Publication date: 7 May 2019

Published in: TURKISH JOURNAL OF MATHEMATICS (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3906/mat-1705-22

zbMATH Keywords

singular pointspectral functioneigenfunction expansionParseval equality\(q\)-Sturm-Liouville operator

Mathematics Subject Classification ID

Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) (34L40) Eigenfunctions, eigenfunction expansions, completeness of eigenfunctions of ordinary differential operators (34L10) Difference equations, scaling ((q)-differences) (39A13) (q)-gamma functions, (q)-beta functions and integrals (33D05)

Related Items (13)

On expansion in eigenfunction for Dirac systems on the unbounded time scales ⋮ Eigenfunction expansion in the singular case for q-Sturm-Liouville operators ⋮ On a $q$-analogue of the Sturm-Liouville operator with discontinuity conditions ⋮ Unnamed Item ⋮ The Parseval identity for \(q\)-Sturm-Liouville problems with transmission conditions ⋮ On the resolvent of singular q-Sturm-Liouville operators ⋮ q−Hamiltonian systems ⋮ Extensions of the matrix-valued q−Sturm–Liouville operators ⋮ Uniqueness for an inverse quantum-Dirac problem with given Weyl function ⋮ On a spectral theory of singular Hahn difference equation of a Sturm‐Liouville type problem with transmission conditions ⋮ Spectral theory of singular Hahn difference equation of the Sturm-Liouville type ⋮ The spectral expansion for the Hahn–Dirac system on the whole line ⋮ Unnamed Item

Cites Work

• \(q\)-fractional calculus and equations
• Deformed Heisenberg algebra: origin of \(q\)-calculus
• q-Titchmarsh-Weyl theory: series expansion
• Beiträge zur Theorie der Heineschen Reihen. Die 24 Integrale der hypergeometrischen q‐Differenzengleichung. Das q‐Analogon der Laplace‐Transformation
• Quantum calculus
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