Selfadjoint Extensions with Several Gaps: Finite Deficiency Indices

  • J.F. Brasche
  • M.M. Malamud
  • H. Neidhardt
Conference paper
Part of the Operator Theory: Advances and Applications book series (OT, volume 162)


Let A be a closed symmetric operator on a separable Hilbert space with equal finite deficiency indices n(A) < ∞ and let J be an open subset of ℝ. It is shown that if there is a self-adjoint extension A0 of A such that J is contained in the resolvent set of A0 and the associated Weyl function of the pair A, A0} is monotone with respect to J, then for any self-adjoint operator R on some separable Hilbert space ℜ obeying dim(ER(J)ℜ) ≤ n(A) there exists a self-adjoint extension à such that the spectral parts ÃJ and RJ are unitarily equivalent. The result generalizes a corresponding result of M.G. Krein for a single gap.


symmetric operators self-adjoint extensions abstract boundary conditions Weyl function 


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Copyright information

© Birkhäuser Verlag Basel/Switzerland 2005

Authors and Affiliations

  • J.F. Brasche
    • 1
  • M.M. Malamud
    • 2
  • H. Neidhardt
    • 3
  1. 1.Institut für MathematikTU ClausthalClausthal-ZellerfeldGermany
  2. 2.Department of MathematicsDonetsk National UniversityDonetskUkraine
  3. 3.Weierstrass Institute for Applied Analysis and Stochastics (WIAS)BerlinGermany

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