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

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.

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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

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
2. S Kotani, M Krishna, “Almost periodicity of some random potentials”, Journal of Functional Analysis, 78:2 (1988), 390
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
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
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
6. F. Gesztesy, H. Holden, B. Simon, “Absolute summability of the trace relation for certain Schrödinger operators”, Comm Math Phys, 168:1 (1995), 137
7. Mikhail Sodin, Peter Yuditskii, “Almost periodic Sturm-Liouville operators with Cantor homogeneous spectrum”, Comment Math Helv, 70:1 (1995), 639
8. Fritz Gesztesy, Barry Simon, “The xi function”, Acta Math, 176:1 (1996), 49
9. Khasanov A., Yakhshimuratov A., “Almost Periodic of Infinite-Zone Potentials of the Operator Dirac”, Dokl. Akad. Nauk, 350:6 (1996), 746–748
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
11. de Monvel A., Egorova I., “On Solutions of Nonlinear Schrodinger Equations with Cantor-Type Spectrum”, J. Anal. Math., 72 (1997), 1–20
12. Fritz Gesztesy, Peter Yuditskii, “Spectral properties of a class of reflectionless Schrödinger operators”, Journal of Functional Analysis, 241:2 (2006), 486
13. RUSSELL JOHNSON, LUCA ZAMPOGNI, “SOME REMARKS CONCERNING REFLECTIONLESS Sturm–Liouville POTENTIALS”, Stoch. Dyn, 08:03 (2008), 413
14. Fritz Gesztesy, Maxim Zinchenko, “Local spectral properties of reflectionless Jacobi, CMV, and Schrödinger operators”, Journal of Differential Equations, 246:1 (2009), 78
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.
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