On the divergence of expansions in systems of root functions of the Sturm-Liouville operator with degenerate boundary conditions

We consider the spectral problem generated by the Sturm-Liouville operator with an arbitrary complex-valued potential q(x) ∈ L 1(0, π) and with degenerate boundary conditions. We show that, under some additional condition, the system of root functions of that operator is not a basis in the space L 2(0, π).