On the Riesz basis property of the root functions in certain regular boundary value problems

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 spaceL₂(0, 1).Translated fromMatematicheskie Zametki, Vol. 64, No. 4, pp. 558–563, October, 1998.