On the Riesz Basisness of Systems Composed of Root Functions of Periodic Boundary Value Problems

Abstract

We consider the nonself-adjoint Sturm-Liouville operator with $q\in L_1[\mathrm{0,1}]$ and either periodic or antiperiodic boundary conditions. We obtain necessary and sufficient conditions for systems of root functions of these operators to be a Riesz basis in $L_2[\mathrm{0,1}]$ in terms of the Fourier coefficients of $q$.