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On nonsymmetric rank one singular perturbations of selfadjoint operators


We consider nonsymmetric rank one singular perturbations of a selfadjoint operator, i.e., an expression of the form $\tilde A=A+\alpha\left\langle\cdot,\omega_1\right\rangle\omega_2$, $\omega_1\not=\omega_2$, $\alpha\in{\mathbb C}$, in a general case $\omega_1,\omega_2\in{\mathcal H}_{-2}$. Using a constructive description of the perturbed operator $\tilde A$, we investigate some spectral and approximations properties of $\tilde A$. The wave operators corresponding to the couple $A$, $\tilde A$ and a series of examples are also presented.

Key words: Singular perturbation, nonsymmetric perturbations, eigenvalue problem, M. Krein's formula.

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TitleOn nonsymmetric rank one singular perturbations of selfadjoint operators
SourceMethods Funct. Anal. Topology, Vol. 22 (2016), no. 2, 137-151
MathSciNet   MR3522856
zbMATH 06665384
Milestones  Received 22/09/2015; Revised 23/02/2016
CopyrightThe Author(s) 2016 (CC BY-SA)

Authors Information

Mykola Dudkin
National Technical University of Ukraine "Kyiv Polytechnic Institute", 37 Prospect Peremogy, Kyiv, 03056, Ukraine

Tetiana Vdovenko
National Technical University of Ukraine "Kyiv Polytechnic Institute", 37 Prospect Peremogy, Kyiv, 03056, Ukraine

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Mykola Dudkin and Tetiana Vdovenko, On nonsymmetric rank one singular perturbations of selfadjoint operators, Methods Funct. Anal. Topology 22 (2016), no. 2, 137-151.


@article {MFAT841,
    AUTHOR = {Dudkin, Mykola and Vdovenko, Tetiana},
     TITLE = {On nonsymmetric rank one singular perturbations of selfadjoint operators},
   JOURNAL = {Methods Funct. Anal. Topology},
  FJOURNAL = {Methods of Functional Analysis and Topology},
    VOLUME = {22},
      YEAR = {2016},
    NUMBER = {2},
     PAGES = {137-151},
      ISSN = {1029-3531},
  MRNUMBER = {MR3522856},
 ZBLNUMBER = {06665384},
       URL = {},


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