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 ∈ L 1 [ 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 [ 0,1 ] in terms of the Fourier coefficients of q. © 2015 Alp Arslan Kraç.