On the Riesz basisness of the root functions of the nonself-adjoint Sturm-Liouville operator
KünyeVELIEV, O.A., DERNEK, N. (2005). On the Riesz basisness of the root functions of the nonself-adjoint Sturm-Liouville operator. Israel Journal of Mathematics, 145 (1), pp. 113-123. http://dx.doi.org/10.1007/BF02786687.
In this article we obtain the asymptotic formulas for eigenfunctions and eigenvalues of the nonself-adjoint Sturm-Liouville operators with periodic and antiperiodic boundary conditions, when the potential is an arbitrary summable complex-valued function. Then using these asymptotic formulas, we find the conditions on Fourier coefficients of the potential for which the eigenfunctions and associated functions of these operators form a Riesz basis in L-2(0, 1).