Abstract
The differential operatorly=y″+q(x)y with periodic (antiperiodic) boundary conditions that are not strongly regular is studied. It is assumed thatq(x) is a complex-valued function of classC (4)[0, 1] andq(0)≠q(1). We prove that the system of root functions of this operator forms a Riesz basis in the spaceL 2(0, 1).
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Translated fromMatematicheskie Zametki, Vol. 64, No. 4, pp. 558–563, October, 1998.
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Kerimov, N.B., Mamedov, K.R. On the Riesz basis property of the root functions in certain regular boundary value problems. Math Notes 64, 483–487 (1998). https://doi.org/10.1007/BF02314629
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DOI: https://doi.org/10.1007/BF02314629