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Izv. Akad. Nauk SSSR Ser. Mat., 1982, Volume 46, Issue 1, Pages 56–87 (Mi izv1605)  

This article is cited in 12 scientific papers (total in 12 papers)

Approximation of infinite-zone potentials by finite-zone potentials

B. M. Levitan


Abstract: In this paper it is proved that each infinite-zone potential of the class considered in the paper “Almost periodicity of infinite-zone potentials” (Izv. Akad. Nauk SSSR Ser. Mat., 1981, v. 45, № 2, pp. 291–320) is the uniform limit of finite-zone potentials on the entire real line. The proof is based on a detailed study of the problem of Jacobi inversion on a two-sheeted Riemann surface with an infinite number of branch points.
Bibliography: 5 titles.

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English version:
Mathematics of the USSR-Izvestiya, 1983, 20:1, 55–87

Bibliographic databases:

UDC: 01.01.01
MSC: Primary 34B25, 34B30; Secondary 30D30
Received: 12.01.1981

Citation: B. M. Levitan, “Approximation of infinite-zone potentials by finite-zone potentials”, Izv. Akad. Nauk SSSR Ser. Mat., 46:1 (1982), 56–87; Math. USSR-Izv., 20:1 (1983), 55–87

Citation in format AMSBIB
\Bibitem{Lev82}
\by B.~M.~Levitan
\paper Approximation of infinite-zone potentials by finite-zone potentials
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1982
\vol 46
\issue 1
\pages 56--87
\mathnet{http://mi.mathnet.ru/izv1605}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=643893}
\zmath{https://zbmath.org/?q=an:0517.34037|0496.35008}
\transl
\jour Math. USSR-Izv.
\yr 1983
\vol 20
\issue 1
\pages 55--87
\crossref{https://doi.org/10.1070/IM1983v020n01ABEH001339}


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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. D. Schenk, M. A. Shubin, “Asymptotic expansion of the state density and the spectral function of a Hill operator”, Math. USSR-Sb., 56:2 (1987), 473–490  mathnet  crossref  mathscinet  zmath
    2. D. Schenk, M. A. Shubin, “Asymptotic expansion of the spectral function of the Hill operator”, Funct. Anal. Appl., 20:1 (1986), 78–79  mathnet  crossref  mathscinet  zmath  isi
    3. Walter Craig, “The trace formula for Schrödinger operators on the line”, Comm Math Phys, 126:2 (1989), 379  crossref  mathscinet  zmath
    4. Y.Colin de Verdière, Th Kappeler, “On double eigenvalues of Hill's operator”, Journal of Functional Analysis, 86:1 (1989), 127  crossref
    5. Fritz Gesztesy, Peter Yuditskii, “Spectral properties of a class of reflectionless Schrödinger operators”, Journal of Functional Analysis, 241:2 (2006), 486  crossref
    6. RUSSELL JOHNSON, LUCA ZAMPOGNI, “SOME REMARKS CONCERNING REFLECTIONLESS Sturm–Liouville POTENTIALS”, Stoch. Dyn, 08:03 (2008), 413  crossref
    7. Fritz Gesztesy, Maxim Zinchenko, “Local spectral properties of reflectionless Jacobi, CMV, and Schrödinger operators”, Journal of Differential Equations, 246:1 (2009), 78  crossref
    8. R. Johnson, L. Zampogni, “On the Camassa–Holm and K–dV Hierarchies”, J Dyn Diff Equat, 2010  crossref
    9. Katrin Grunert, “The transformation operator for Schrödinger operators on almost periodic infinite-gap backgrounds”, Journal of Differential Equations, 250:8 (2011), 3534  crossref
    10. Katrin Grunert, “Scattering theory for Schrödinger operators on steplike, almost periodic infinite-gap backgrounds”, Journal of Differential Equations, 254:6 (2013), 2556  crossref
    11. G. Friesecke, A. Mikikits-Leitner, “Cnoidal Waves on Fermi–Pasta–Ulam Lattices”, J Dyn Diff Equat, 2014  crossref
    12. 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
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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