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Matematicheskie Zametki, 2009, Volume 85, Issue 3, Pages 451–455
DOI: https://doi.org/10.4213/mzm4670 (Mi mzm4670) 		 
This article is cited in 2 scientific papers (total in 2 papers)

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

M. M. Faddeev

Saint-Petersburg State University
Full-text PDF (409 kB) Citations (2)
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DOI: https://doi.org/10.4213/mzm4670
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, PT-symmetric potential, similarity to a self-adjoint operator.
Received: 27.02.2008
English version:
Mathematical Notes, 2009, Volume 85, Issue 3, Pages 437–440
DOI: https://doi.org/10.1134/S0001434609030146
Bibliographic databases:
UDC: 517.948.35
Language: Russian
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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  • https://www.mathnet.ru/eng/mzm/v85/i3/p451
    • This publication is cited in the following 2 articles:
    1. O. O. Pokutnyi, “Boundary-Value Problems for the Evolutionary Schrödinger Equation. I”, J Math Sci, 249:4 (2020), 647  crossref
    2. Yan Zh., “Complex 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
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Математические заметки Mathematical Notes
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