Geodesic
On a $q$-boundary value problem with discontinuity conditions
Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematika, mehanika, fizika, Tome 13 (2021) no. 4, pp. 5-12

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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. 
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D. Karahan; K. R. Mamedov. On a $q$-boundary value problem with discontinuity conditions. Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematika, mehanika, fizika, Tome 13 (2021) no. 4, pp. 5-12. http://geodesic.mathdoc.fr/item/VYURM_2021_13_4_a0/