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Izv. Akad. Nauk SSSR Ser. Mat., 1967, Volume 31, Issue 5, Pages 965–976 (Mi izv2571)  

This article is cited in 8 scientific papers (total in 8 papers)

On inverse Sturm–Liouville problems on a finite segment

V. V. Zhikov


Abstract: A necessary and sufficient condition for reconstructing the differential operator $-y"+dF\cdot y$, where $F$ is a function of bounded variation, from the spectra of two boundary value problems on the segment $[0,\pi]$, is established in this paper.

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English version:
Mathematics of the USSR-Izvestiya, 1967, 1:5, 923–934

Bibliographic databases:

UDC: 517.9
MSC: 34B24, 34A55, 15A29
Received: 24.02.1966

Citation: V. V. Zhikov, “On inverse Sturm–Liouville problems on a finite segment”, Izv. Akad. Nauk SSSR Ser. Mat., 31:5 (1967), 965–976; Math. USSR-Izv., 1:5 (1967), 923–934

Citation in format AMSBIB
\Bibitem{Zhi67}
\by V.~V.~Zhikov
\paper On inverse Sturm--Liouville problems on a finite segment
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1967
\vol 31
\issue 5
\pages 965--976
\mathnet{http://mi.mathnet.ru/izv2571}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=217365}
\zmath{https://zbmath.org/?q=an:0174.39401}
\transl
\jour Math. USSR-Izv.
\yr 1967
\vol 1
\issue 5
\pages 923--934
\crossref{https://doi.org/10.1070/IM1967v001n05ABEH000593}


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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. Ole H. Hald, “Inverse eigenvalue problems for layered media”, Comm Pure Appl Math, 30:1 (1977), 69  crossref  mathscinet  zmath
    2. Ole H. Hald, “The inverse Sturm-Liouville problem with symmetric potentials”, Acta Math, 141:1 (1978), 263  crossref  mathscinet  zmath
    3. Ole H. Hald, “Discontinuous inverse eigenvalue problems”, Comm Pure Appl Math, 37:5 (1984), 539  crossref  mathscinet  zmath
    4. O H Hald, J R McLaughlin, Inverse Probl, 5:3 (1989), 307  crossref  mathscinet  zmath  adsnasa  isi
    5. Vinokurov V.A., Sadovnichii V.A., “The uniform equiconvergence of the Fourier series in the eigenfunctions of the first boundary value problem and of the trigonometric Fourier series”, Doklady Mathematics, 64:2 (2001), 248–252  isi  elib
    6. M. I. Neiman-Zade, A. M. Savchuk, “Schrödinger Operators with Singular Potentials”, Proc. Steklov Inst. Math., 236 (2002), 250–259  mathnet  mathscinet  zmath
    7. T. N. Harutyunyan, “The eigenvalue function of a family of Sturm–Liouville operators”, Izv. Math., 74:3 (2010), 439–459  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    8. T. N. Harutyunyan, “Asymptotics of the norming constants of the SturmLiouville problem”, Uch. zapiski EGU, ser. Fizika i Matematika, 2013, no. 3, 3–11  mathnet
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