On the Riesz Basisness of Systems Composed of Root Functions of Periodic   Boundary Value Problems
  In this paper, we consider the nonselfadjoint Sturm Liouville operator with 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 in terms of the Fourier coefficients of q. 
Alp Arslan Kirac
math.SP