Abstract:
In this paper, we studied q-analogue of Sturm-Liouville boundary value problem on a finite interval having a discontinuity in an interior point. We proved that the q-Sturm-Liouville problem is self-adjoint in a modified Hilbert space. We investigated spectral properties of the eigenvalues and the eigenfunctions of q-Sturm-Liouville boundary value problem. We shown that eigenfunctions of q-Sturm-Liouville boundary value problem are in the form of a complete system. Finally, we proved a sampling theorem for integral transforms whose kernels are basic functions and the integral is of Jackson's type.
Keywords:q-Sturm-Liouville operator, self-adjoint operator, completeness of eigenfunctions, sampling theory.
Citation:
D. Karahan, K. R. Mamedov, “On a q-boundary value problem with discontinuity conditions”, Vestn. Yuzhno-Ural. Gos. Un-ta. Ser. Matem. Mekh. Fiz., 13:4 (2021), 5–12
\Bibitem{KarMam21}
\by D.~Karahan, K.~R.~Mamedov
\paper On a $q$-boundary value problem with discontinuity conditions
\jour Vestn. Yuzhno-Ural. Gos. Un-ta. Ser. Matem. Mekh. Fiz.
\yr 2021
\vol 13
\issue 4
\pages 5--12
\mathnet{http://mi.mathnet.ru/vyurm495}
\crossref{https://doi.org/10.14529/mmph210401}
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https://www.mathnet.ru/eng/vyurm495
https://www.mathnet.ru/eng/vyurm/v13/i4/p5
This publication is cited in the following 6 articles:
Bilender P. Allahverdiev, Hüseyin Tuna, Hamlet A. Isayev, “The Resolvent of Impulsive Singular Hahn–Sturm–Liouville Operators”, Annales Mathematicae Silesianae, 2024
B. P. Allahverdiev, H. Tuna, “Existence theorem for a fractal Sturm–Liouville problem”, Vladikavk. matem. zhurn., 26:1 (2024), 27–35
Bilender P. Allahverdiev, Huseyin Tuna, Hamlet A Isayev, “Impulsive regular q-Dirac systems”, ejde, 2023:01-?? (2023), 74
Martin Bohner, Ayça Çetinkaya, “Uniqueness for an Inverse Quantum-Dirac Problem with Given Weyl Function”, Tatra Mountains Mathematical Publications, 84:2 (2023), 1
D. Karahan, “On a q-analogue of the Sturm–Liouville operator with discontinuity conditions”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 26:3 (2022), 407–418
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