An analytic characterization of the eigenvalues of self-adjoint extensions

Let A be a self-adjoint extension in K of a fixed symmetric operator A in K ⊆ K. An analytic characterization of the eigenvalues of A is given in terms of the Q-function and the parameter function in the Krein–Naimark formula. Here K and K are Krein spaces and it is assumed that A 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. © 2006 Elsevier Inc. All rights reserved.