Geodesic
On the Riesz basis property of the root functions in certain regular boundary value problems
Matematičeskie zametki, Tome 64 (1998) no. 4, pp. 558-563.

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The differential operator $ly=y''+q(x)y$ with periodic (antiperiodic) boundary conditions that are not strongly regular is studied. It is assumed that $q(x)$ is a complex-valued function of class $C^{(4)}[0,1]$ and $q(0)\ne q(1)$. We prove that the system of root functions of this operator forms a Riesz basis in the space $L_2(0,1)$. 
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N. B. Kerimov; Kh. R. Mamedov. On the Riesz basis property of the root functions in certain regular boundary value problems. Matematičeskie zametki, Tome 64 (1998) no. 4, pp. 558-563. http://geodesic.mathdoc.fr/item/MZM_1998_64_4_a7/

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