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An analytic characterization of the eigenvalues of self-adjoint extensions

Authors
Journal
Journal of Functional Analysis
0022-1236
Publisher
Elsevier
Publication Date
Volume
242
Issue
2
Identifiers
DOI: 10.1016/j.jfa.2006.09.011
Keywords
  • Krein Space
  • Self-Adjoint Extension
  • Krein–Naimark Formula
  • (Locally) Definitizable Operator
  • (Local) Generalized Nevanlinna Function
  • Generalized Pole And Zero
  • Boundary Value Problem

Abstract

Abstract 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.

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