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Mat. Zametki, 2009, Volume 85, Issue 3, Pages 451–455 (Mi mz4670)  

This article is cited in 1 scientific paper (total in 1 paper)

On Spectral Properties of the Discrete Schrödinger Operator with Pure Imaginary Finite Potential

M. M. Faddeev

Saint-Petersburg State University

Abstract: In this paper, we consider the spectral properties of the discrete Schrödinger operator in the space of square integrable two-sided sequences with a pure imaginary potential of finite rank with zero mean value. We show that if such potentials are small, then the spectrum of the operator under study coincides with the spectrum of the unperturbed operator, and the operator itself is similar to a self-adjoint operator.

Keywords: discrete Schrödinger operator, spectral problem, $\mathscr{PT}$-symmetric potential, similarity to a self-adjoint operator

DOI: https://doi.org/10.4213/mzm4670

Full text: PDF file (409 kB)
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English version:
Mathematical Notes, 2009, 85:3, 437–440

Bibliographic databases:

UDC: 517.948.35
Received: 27.02.2008

Citation: M. M. Faddeev, “On Spectral Properties of the Discrete Schrödinger Operator with Pure Imaginary Finite Potential”, Mat. Zametki, 85:3 (2009), 451–455; Math. Notes, 85:3 (2009), 437–440

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Yan Zh., “Complex $\mathcal{PT}$-symmetric extensions of the nonlinear ultra-short light pulse model”, J. Phys. A, 45:44 (2012), 444035  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
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