An analytic characterization of the eigenvalues of self-adjoint extensions
In this paper, the analytic characterization of the eigenvalues of self-adjoint extensions is generalized. Also, a class of boundary value problems with boundary conditions depending on the spectral parameter is analyzed, which is closely connected with the self-adjoint extensions of a symmetric operator. The paper recalls the necessary definitions and basic properties of self-adjoint operators, introduces the concept of generalized values of local generalized Nevanlinna functions, and studies the behaviour of these functions at such points. The main results are contained in the fourth section of the paper; in the last section, as an application of the results, a class of abstract eigenvalue dependent boundary value problems is investigated. Also, as an example, a singular Sturm-Liouville operator with the signum function as indefinite weight in a Krein space is studied.
(locally) generalized Nevanlinna function
scientific article; zbMATH DE number 5116377
scientific article