Common eigenvalue problem and periodic Schrödinger operators (Q1300172)

The authors study families of selfadjoint extensions of a symmetric operator \(A_0\) in a Hilbert space with equal deficiency indices. If \(A_0\) has a purely residual spectrum, the set of eigenvalues common to all these selfadjoint extensions is described using the technique of boundary value spaces (BVS). This result is used to present a new view point on the spectral theory of periodic differential operators. As an application and illustration of the method, the one-dimensional Schrödinger operator with local point interactions is considered. It should be mentioned that the paper also contains some results with full proofs from original papers of the Soviet School e.g. on the boundary value space technique which have not been available easily by now.