L. A. Pastur, V. A. Tkachenko, “Geometry of the spectrum of the one-dimensional Schrödinger equation with a periodic complex-valued potential”, Mat. Zametki, 50:4 (1991), 88–95; Math. Notes, 50:4 (1991), 1045

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Matematicheskie Zametki, 1991, Volume 50, Issue 4, Pages 88–95 (Mi mzm3089)

This article is cited in 11 scientific papers (total in 11 papers)

Geometry of the spectrum of the one-dimensional Schrödinger equation with a periodic complex-valued potential

L. A. Pastur, V. A. Tkachenko

Physical Engineering Institute of Low Temperatures, UkrSSR Academy of Sciences

Full-text PDF (630 kB) Citations (11)

Received: 14.06.1990

English version:
Mathematical Notes, 1991, Volume 50, Issue 4, Pages 1045–1050
DOI: https://doi.org/10.1007/BF01137736

Bibliographic databases:

UDC: 517

Language: Russian

Citation: L. A. Pastur, V. A. Tkachenko, “Geometry of the spectrum of the one-dimensional Schrödinger equation with a periodic complex-valued potential”, Mat. Zametki, 50:4 (1991), 88–95; Math. Notes, 50:4 (1991), 1045–1050

Citation in format AMSBIB

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\paper Geometry of the spectrum of the one-dimensional Schr\"odinger equation with a periodic complex-valued potential

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\vol 50

\issue 4

\pages 88--95

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\zmath{https://zbmath.org/?q=an:0781.34054|0738.34046}

\transl

\jour Math. Notes

\yr 1991

\vol 50

\issue 4

\pages 1045--1050

\crossref{https://doi.org/10.1007/BF01137736}

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Linking options:

https://www.mathnet.ru/eng/mzm3089

https://www.mathnet.ru/eng/mzm/v50/i4/p88

This publication is cited in the following 11 articles:

Hui Lu, Jiangong You, “Global structure of spectra of periodic non-Hermitian Jacobi operators”, Sci. China Math., 2024
Oktay Veliev, Non-self-adjoint Schrödinger Operator with a Periodic Potential, 2021, 15
William A. Haese-Hill, Martin A. Hallnäs, Alexander P. Veselov, “On the Spectra of Real and Complex Lamé Operators”, SIGMA, 13 (2017), 049, 23 pp.
Gesztesy F. Tkachenko V., “A Schauder and Riesz Basis Criterion for Non-Self-Adjoint Schrodinger Operators with Periodic and Antiperiodic Boundary Conditions”, J. Differ. Equ., 253:2 (2012), 400–437
S. Longhi, “Spectral singularities and Bragg scattering in complex crystals”, Phys. Rev. A, 81:2 (2010)
Fritz Gesztesy, Vadim Trachenko, “A criterion for Hill operators to be spectral operators of scalar type”, J Anal Math, 107:1 (2009), 287
Fritz Gesztesy, Vadim Tkachenko, “When is a non-self-adjoint Hill operator a spectral operator of scalar type?⁎⁎Based upon work supported by the US National Science Foundation under Grant No. DMS-0405526 and the Research Council and the Office of Research of the University of Missouri–Columbia.”, Comptes Rendus. Mathématique, 343:4 (2006), 239
Volodymyr Batchenko, Fritz Gesztesy, “On the spectrum of Schrödinger operators with quasi-periodic algebro-geometric KDV potentials”, J. Anal. Math., 95:1 (2005), 333
Gesztesy, F, “Elliptic algebro-geometric solutions of the KdV and AKNS hierarchies - An analytic approach”, Bulletin of the American Mathematical Society, 35:4 (1998), 271
A. L. Mironov, V. L. Oleinik, “Limits of applicability of the tight binding approximation for complex-valued potential function”, Theoret. and Math. Phys., 112:3 (1997), 1157–1171
Fritz Gesztesy, Rudi Weikard, “Picard potentials and Hill's equation on a torus”, Acta Math., 176:1 (1996), 73

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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