Basis Properties of the System of Root Functions of the Sturm–Liouville Operator with Degenerate Boundary Conditions: I

Resumo

The spectral problem for the Sturm–Liouville operator with an arbitrary complex-valued potential q(x) of the class L¹(0, π) and degenerate boundary conditions is considered. We prove that the system of root functions of this operator is not a basis in the space L²(0, π).