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Schrödinger operators with non-symmetric zero-range potentials


Non-self-adjoint Schrödinger operators $A_{\mathbf{T}}$ which correspond to non-symmetric zero-range potentials are investigated. For a given $A_{\mathbf{T}}$, a description of non-real eigenvalues, spectral singularities and exceptional points are obtained; the possibility of interpretation of $A_{\mathbf{T}}$ as a self-adjoint operator in a Krein space is studied, the problem of similarity of $A_{\mathbf{T}}$ to a self-adjoint operator in a Hilbert space is solved.

Key words: Non-self-adjoint Schrödinger operators, zero-range potentials, Krein spaces, similarity to a self-adjoint operator.

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TitleSchrödinger operators with non-symmetric zero-range potentials
SourceMethods Funct. Anal. Topology, Vol. 20 (2014), no. 1, 34-49
MathSciNet MR3242121
zbMATH 1313.81011
MilestonesReceived 02/09/2013; Revised 20/09/2013
CopyrightThe Author(s) 2014 (CC BY-SA)

Authors Information

A. Grod
Institute of Mathematics, National Academy of Sciences of Ukraine, 3 Tereshchenkivs'ka, Kyiv, 01601, Ukraine

S. Kuzhel
AGH University of Science and Technology, Krako 

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A. Grod and S. Kuzhel, Schrödinger operators with non-symmetric zero-range potentials, Methods Funct. Anal. Topology 20 (2014), no. 1, 34-49.


@article {MFAT706,
    AUTHOR = {Grod, A. and Kuzhel, S.},
     TITLE = {Schrödinger operators with non-symmetric zero-range potentials},
   JOURNAL = {Methods Funct. Anal. Topology},
  FJOURNAL = {Methods of Functional Analysis and Topology},
    VOLUME = {20},
      YEAR = {2014},
    NUMBER = {1},
     PAGES = {34-49},
      ISSN = {1029-3531},
  MRNUMBER = {MR3242121},
 ZBLNUMBER = {1313.81011},
       URL = {},

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