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Mat. Sb. (N.S.), 1984, Volume 123(165), Number 1, Pages 69–91 (Mi msb1985)  

This article is cited in 15 scientific papers (total in 15 papers)

On the closure of the set of finite-zone potentials

B. M. Levitan


Abstract: A special class of almost-periodic potentials of the one-dimensional Schrödinger operator is studied. These potentials are limits of finite-zone potentials. In contrast to previous work of the author in which a class of almost-periodic potentials was considered with lacunae in the spectrum having a single limit point at infinity, in this paper the case is studied where the lacunae in the spectrum also have finite limit points. There may be infinitely many of the latter.
Figures: 2.
Bibliography: 10 titles.

Full text: PDF file (1012 kB)
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English version:
Mathematics of the USSR-Sbornik, 1985, 51:1, 67–89

Bibliographic databases:

UDC: 517.9
MSC: Primary 35J10; Secondary 35P25
Received: 25.03.1983

Citation: B. M. Levitan, “On the closure of the set of finite-zone potentials”, Mat. Sb. (N.S.), 123(165):1 (1984), 69–91; Math. USSR-Sb., 51:1 (1985), 67–89

Citation in format AMSBIB
\Bibitem{Lev84}
\by B.~M.~Levitan
\paper On the closure of the set of finite-zone potentials
\jour Mat. Sb. (N.S.)
\yr 1984
\vol 123(165)
\issue 1
\pages 69--91
\mathnet{http://mi.mathnet.ru/msb1985}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=728930}
\zmath{https://zbmath.org/?q=an:0589.34026}
\transl
\jour Math. USSR-Sb.
\yr 1985
\vol 51
\issue 1
\pages 67--89
\crossref{https://doi.org/10.1070/SM1985v051n01ABEH002847}


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

    This publication is cited in the following articles:
    1. Danielyan A., “On the Width of the Strip of Regularity of the Finite-Zone Dirac Operator”, Vestn. Mosk. Univ. Seriya 1 Mat. Mekhanika, 1987, no. 3, 81–82  mathscinet  zmath  isi
    2. S Kotani, M Krishna, “Almost periodicity of some random potentials”, Journal of Functional Analysis, 78:2 (1988), 390  crossref
    3. Yegorova I., “On a Class of Almost-Periodic Solutions of Korteweg-Devries with Nowhere Dense Spectrum”, Dokl. Akad. Nauk, 323:2 (1992), 219–222  mathnet  isi
    4. Sodin M., Yuditskii P., “Almost-Periodic Sturm-Liouville Operators with Cantorian Homogeneous Spectra and Pseudocontinuable Weyl Functions”, Dokl. Akad. Nauk, 339:6 (1994), 736–738  mathnet  mathscinet  zmath  isi
    5. Sodin M., Yuditskii P., “Infinite-Dimensional Real Jacobi Inversion Problem and Hardy-Spaces of Character-Automorphic Functions”, Dokl. Akad. Nauk, 335:2 (1994), 161–163  mathnet  mathscinet  zmath  isi
    6. F. Gesztesy, H. Holden, B. Simon, “Absolute summability of the trace relation for certain Schrödinger operators”, Comm Math Phys, 168:1 (1995), 137  crossref  mathscinet  zmath  adsnasa
    7. Mikhail Sodin, Peter Yuditskii, “Almost periodic Sturm-Liouville operators with Cantor homogeneous spectrum”, Comment Math Helv, 70:1 (1995), 639  crossref  mathscinet  zmath  isi
    8. Fritz Gesztesy, Barry Simon, “The xi function”, Acta Math, 176:1 (1996), 49  crossref  mathscinet  zmath  isi
    9. Khasanov A., Yakhshimuratov A., “Almost Periodic of Infinite-Zone Potentials of the Operator Dirac”, Dokl. Akad. Nauk, 350:6 (1996), 746–748  mathnet  mathscinet  zmath  isi
    10. Mikhail Sodin, Peter Yuditskii, “Almost periodic Jacobi matrices with homogeneous spectrum, infinite dimensional Jacobi inversion, and hardy spaces of character-automorphic functions”, J Geom Anal, 7:3 (1997), 387  crossref
    11. de Monvel A., Egorova I., “On Solutions of Nonlinear Schrodinger Equations with Cantor-Type Spectrum”, J. Anal. Math., 72 (1997), 1–20  crossref  mathscinet  zmath  isi
    12. Fritz Gesztesy, Peter Yuditskii, “Spectral properties of a class of reflectionless Schrödinger operators”, Journal of Functional Analysis, 241:2 (2006), 486  crossref
    13. RUSSELL JOHNSON, LUCA ZAMPOGNI, “SOME REMARKS CONCERNING REFLECTIONLESS Sturm–Liouville POTENTIALS”, Stoch. Dyn, 08:03 (2008), 413  crossref
    14. Fritz Gesztesy, Maxim Zinchenko, “Local spectral properties of reflectionless Jacobi, CMV, and Schrödinger operators”, Journal of Differential Equations, 246:1 (2009), 78  crossref
    15. Russell Johnson, Luca Zampogni, “The Sturm–Liouville Hierarchy of Evolution Equations and Limits of Algebro-Geometric Initial Data”, SIGMA, 10 (2014), 020, 23 pp.  mathnet  crossref  mathscinet
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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