On the absence of the basis property for the root function system of the Sturm–Liouville operator with degenerate boundary conditions

Resumo

The eigenvalue problem generated by the Sturm–Liouville equation on the interval (0, π) with degenerate boundary conditions is considered. Under certain conditions imposed on the spectrum, it is shown that the system of eigen- and associated functions is not a basis in L₂(0, π).