An analytic characterization of the eigenvalues of self-adjoint extensions

Let be a self-adjoint extension in of a fixed symmetric operator A in . An analytic characterization of the eigenvalues of is given in terms of the Q-function and the parameter function in the Krein–Naimark formula. Here K and are Krein spaces and it is assumed that locally has the same spectral properties as a self-adjoint operator in a Pontryagin space. The general results are applied to a class of boundary value problems with λ-dependent boundary conditions.