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# Schrödinger operators with non-symmetric zero-range potentials

### Abstract

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.

### Article Information

 Title Schrödinger operators with non-symmetric zero-range potentials Source Methods Funct. Anal. Topology, Vol. 20 (2014), no. 1, 34-49 MathSciNet MR3242121 zbMATH 1313.81011 Milestones Received 02/09/2013; Revised 20/09/2013 Copyright The 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

### Citation Example

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

### BibTex

@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 = {http://mfat.imath.kiev.ua/article/?id=706},
}