Geodesic
On a $q$-analogue of the Sturm--Liouville operator with discontinuity conditions
Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, Tome 26 (2022) no. 3, pp. 407-418

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In this paper, a $q$-analogue of the Sturm–Liouville problem with discontinuity condition on a finite interval is studied. It is proved that the $q$-Sturm–Liouville problem with discontinuity conditions is self-adjoint in $L_q^2(0,\pi)$. The completeness theorem and the sampling theorem are proved.
Keywords: $q$-Sturm–Liouville operator, completeness of eigenfunctions, self-adjoint operato. 
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     author = {D. Karahan},
     title = {On a $q$-analogue of the {Sturm--Liouville} operator with discontinuity conditions},
     journal = {Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences},
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     year = {2022},
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     url = {http://geodesic.mathdoc.fr/item/VSGTU_2022_26_3_a0/}
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D. Karahan. On a $q$-analogue of the Sturm--Liouville operator with discontinuity conditions. Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, Tome 26 (2022) no. 3, pp. 407-418. http://geodesic.mathdoc.fr/item/VSGTU_2022_26_3_a0/