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An analytic characterization of the eigenvalues of self-adjoint extensions

Behrndt, Jussi; Luger, Annemarie

Preprint-Reihe des Instituts für Mathematik, Technische Universität Berlin

Let à be a self-adjoint extension in K of a fixed symmetric operator A in K ⊆ K. Ananalytic characterization of the eigenvalues of à 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 à 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.