Skip to main content
SpringerLink
Log in

A generalization of Borg’s uniqueness theorems for a symmetric potential to general boundary conditions

  • Mathematics
  • Published:
Doklady Mathematics Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

References

  1. V. A. Ambarzumijan, Z. Phys, No. 53, 690–695 (1929).

    Google Scholar 

  2. G. Borg, Acta Math. 78(1), 1–96 (1946).

    Article  MATH  MathSciNet  Google Scholar 

  3. N. Levinson, Math. Tidsskr. 8, 25–30 (1949).

    MathSciNet  Google Scholar 

  4. V. A. Marchenko, Sturm-Liouville Operators and Their Applications (Naukova Dumka, Kiev, 1977) [in Russian].

    MATH  Google Scholar 

  5. B. M. Levitan, Sturm-Liouville Inverse Problems (Nauka, Moscow, 1984) [in Russian].

    MATH  Google Scholar 

  6. V. A. Yurko, Introduction to the Theory of Inverse Spectral Problems (Fizmatlit, Moscow, 2007) [in Russian].

    Google Scholar 

  7. M. G. Gasymov, I. M. Guseinov, and I. M. Nabiev, Sib. Mat. Zh. 31(6), 46–54 (1990).

    MathSciNet  Google Scholar 

  8. I. M. Guseinov and I. M. Nabiev, Sb. Math. 198(11), 1579–1598 (2007).

    Article  MATH  MathSciNet  Google Scholar 

  9. V. A. Sadovnichii, Ya. T. Sultanaev, and A. M. Akhtyamov, The Inverse Sturm-Luouville Problem with Non-separated Boundary Conditions (Mosk. Gos. Univ., Moscow, 2009) [in Russian].

    Google Scholar 

  10. O. A. Plaksina, Sb. Math. 59(1), 1–23 (1988).

    Article  MATH  MathSciNet  Google Scholar 

  11. O. A. Plaksina, Sb. Math. 64(1), 141–160 (1989).

    Article  MathSciNet  Google Scholar 

  12. M. A. Naimark, Linear Differential Operators (Nauka, Moscow, 1969) [in Russian].

    Google Scholar 

  13. I. M. Nabiev and A. Sh. Shukyurov, Izv. Saratov. Univ. Ser. Mat. Mekh. Inf. 9,Part 1 (4), 36–40 (2009).

    Google Scholar 

  14. A. M. Akhtyamov, A. V. Muftakhov, and A. A. Akhtyamova, Vestn. Udmurt. Univ. Mat. Mekh. Komp’yuter. Nauki 3, 114–129 (2013).

    Google Scholar 

  15. A. M. Akhtyamov, Identification Theory of Boundary Value Problems and Its Applications (Fizmatlit, Moscow, 2009) [in Russian].

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Mechanics and Mathematics Faculty, Moscow State University, Moscow, 119991, Russia

    V. A. Sadovnichii

  2. Institute of Mechanics, Russian Academy of Sciences, ul. Karla Marksa 12, Ufa, 450025, Bashkortostan, Russia

    Ya. T. Sultanaev & A. M. Akhtyamov

  3. Bashkir State Pedagogical University, ul. Oktyabr’skoi revolyutsii 3a, Ufa, 450000, Bashkortostan, Russia

    Ya. T. Sultanaev

  4. Bashkir State University, ul. Zaki Validi 32, Ufa, 450074, Bashkortostan, Russia

    A. M. Akhtyamov

Authors
  1. V. A. Sadovnichii
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ya. T. Sultanaev
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. A. M. Akhtyamov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to V. A. Sadovnichii.

Additional information

Original Russian Text © V.A. Sadovnichii, Ya.T. Sultanaev, A.M. Akhtyamov, 2014, published in Doklady Akademii Nauk, 2014, Vol. 458, No. 3, pp. 264–267.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Sadovnichii, V.A., Sultanaev, Y.T. & Akhtyamov, A.M. A generalization of Borg’s uniqueness theorems for a symmetric potential to general boundary conditions. Dokl. Math. 90, 565–568 (2014). https://doi.org/10.1134/S1064562414060167

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1064562414060167

Keywords

Search

Navigation