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Mathematics of the USSR-Sbornik, 1975, Volume 26, Issue 4, Pages 493–554
DOI: https://doi.org/10.1070/SM1975v026n04ABEH002493 (Mi sm3807) 		 
This article is cited in 187 scientific papers (total in 187 papers)

A characterization of the spectrum of Hill's operator

V. A. Marchenko, I. V. Ostrovskii
English version PDF (2855 kB) Citations (187)
References:
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DOI: https://doi.org/10.1070/SM1975v026n04ABEH002493
Abstract: This article contains a complete derivation of necessary and sufficient conditions which a given sequence of intervals must satisfy in order that a Hill differential operator $L[y]=-y''+v(x)y$, with real, periodic potential $v(x)$, exist, whose spectrum coincides with this sequence of intervals. The proof is based on a specific representation of entire functions $u(z)$ such that the equation $u^2(z)=1$ has only real roots, conformal mappings having properties associated with this representation, and refined asymptotic formulas for the eigenvalues of certain boundary value problems.
Figures: 4.
Bibliography: 17 titles.
Received: 03.02.1975
Russian version:
Matematicheskii Sbornik. Novaya Seriya, 1975, Volume 97(139), Number 4(8), Pages 540–606
Bibliographic databases:
UDC: 517.9
MSC: Primary 34B25, 34B30, 47E05; Secondary 30A64, 30A24, 35Q99
Language: English
Original paper language: Russian
Citation: V. A. Marchenko, I. V. Ostrovskii, “A characterization of the spectrum of Hill's operator”, Mat. Sb. (N.S.), 97(139):4(8) (1975), 540–606; Math. USSR-Sb., 26:4 (1975), 493–554
Citation in format AMSBIB
\Bibitem{MarOst75}
\by V.~A.~Marchenko, I.~V.~Ostrovskii
\paper A~characterization of the spectrum of Hill's operator
\jour Mat. Sb. (N.S.)
\yr 1975
\vol 97(139)
\issue 4(8)
\pages 540--606
\mathnet{http://mi.mathnet.ru/sm3807}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=409965}
\zmath{https://zbmath.org/?q=an:0327.34021}
\transl
\jour Math. USSR-Sb.
\yr 1975
\vol 26
\issue 4
\pages 493--554
\crossref{https://doi.org/10.1070/SM1975v026n04ABEH002493}
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  • https://doi.org/10.1070/SM1975v026n04ABEH002493
  • https://www.mathnet.ru/eng/sm/v139/i4/p540
    • This publication is cited in the following 187 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics
    Statistics & downloads:
    Abstract page:1797
    Russian version PDF:639
    English version PDF:19
    References:80
    First page:1
     
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