Skip to main content

We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.

Close cookie message
Cancel
×
×
Home
  • Home
Article
  • Cited by 20
  • Cited by
    Crossref Citations
    Crossref logo
    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.
    Savchuk, A. M. 2016. Reconstruction of the potential of the Sturm–Liouville operator from a finite set of eigenvalues and normalizing constants. Mathematical Notes, Vol. 99, Issue. 5-6, p. 715.
    Савчук, Артем Маркович and Savchuk, Artem Markovich 2016. Восстановление потенциала оператора Штурма - Лиувилля по конечному набору собственных значений и нормировочных чисел. Математические заметки, Vol. 99, Issue. 5, p. 715.
    Savchuk, A. M. and Shkalikov, A. A. 2013. Uniform stability of the inverse Sturm-Liouville problem with respect to the spectral function in the scale of Sobolev spaces. Proceedings of the Steklov Institute of Mathematics, Vol. 283, Issue. 1, p. 181.
    Pronska, Nataliya 2013. Reconstruction of Energy-Dependent Sturm–Liouville Equations from two Spectra. Integral Equations and Operator Theory, Vol. 76, Issue. 3, p. 403.
    Djakov, Plamen and Mityagin, Boris 2013. Equiconvergence of spectral decompositions of Hill–Schrödinger operators. Journal of Differential Equations, Vol. 255, Issue. 10, p. 3233.
    Hryniv, Rostyslav and Pronska, Nataliya 2012. Inverse spectral problems for energy-dependent Sturm–Liouville equations. Inverse Problems, Vol. 28, Issue. 8, p. 085008.
    Langer, Matthias and Woracek, Harald 2011. A local inverse spectral theorem for Hamiltonian systems. Inverse Problems, Vol. 27, Issue. 5, p. 055002.
    Hryniv, Rostyslav O 2011. Analyticity and uniform stability in the inverse singular Sturm–Liouville spectral problem. Inverse Problems, Vol. 27, Issue. 6, p. 065011.
    Hryniv, Rostyslav O. 2011. Analyticity and uniform stability in the inverse spectral problem for Dirac operators. Journal of Mathematical Physics, Vol. 52, Issue. 6, p. 063513.
    Савчук, Артем Маркович Savchuk, Artem Markovich Шкаликов, Андрей Андреевич and Shkalikov, Andrei Andreevich 2010. Обратные задачи для оператора Штурма - Лиувилля с потенциалами из пространств Соболева. Равномерная устойчивость. Функциональный анализ и его приложения, Vol. 44, Issue. 4, p. 34.
    Hryniv, Rostyslav and Sacks, Paul 2010. Numerical solution of the inverse spectral problem for Bessel operators. Journal of Computational and Applied Mathematics, Vol. 235, Issue. 1, p. 120.
    Savchuk, A. M. and Shkalikov, A. A. 2010. Inverse problems for Sturm—Liouville operators with potentials in Sobolev spaces: Uniform stability. Functional Analysis and Its Applications, Vol. 44, Issue. 4, p. 270.
    Покорный, Юлий Витальевич Pokornyi, Yulii Vitaljevich Зверева, Маргарита Борисовна Zvereva, Margarita Borisovna Шабров, Сергей Александрович and Shabrov, Sergey Aleksandrovich 2008. Осцилляционная теория Штурма - Лиувилля для импульсных задач. Успехи математических наук, Vol. 63, Issue. 1, p. 111.
    Savchuk, A. M. and Shkalikov, A. A. 2008. On the properties of maps connected with inverse Sturm-Liouville problems. Proceedings of the Steklov Institute of Mathematics, Vol. 260, Issue. 1, p. 218.
    Albeverio, S. Hryniv, R. and Mykytyuk, Ya. 2008. Reconstruction of radial Dirac and Schrödinger operators from two spectra. Journal of Mathematical Analysis and Applications, Vol. 339, Issue. 1, p. 45.
    Albeverio, S Hryniv, R O and Nizhnik, L P 2007. Inverse spectral problems for non-local Sturm–Liouville operators. Inverse Problems, Vol. 23, Issue. 2, p. 523.
    Albeverio, S Binding, P Hryniv, R and Mykytyuk, Ya 2007. Inverse spectral problems for coupled oscillating systems. Inverse Problems, Vol. 23, Issue. 3, p. 1181.
    Hryniv, R.O. and Mykytyuk, Y.V. 2006. Eigenvalue asymptotics for Sturm–Liouville operators with singular potentials. Journal of Functional Analysis, Vol. 238, Issue. 1, p. 27.
    Савчук, Артем Маркович Savchuk, Artem Markovich Шкаликов, Андрей Андреевич and Shkalikov, Andrei Andreevich 2006. О собственных значениях оператора Штурма - Лиувилля с потенциалами из пространств Соболева. Математические заметки, Vol. 80, Issue. 6, p. 864.
    Savchuk, A. M. and Shkalikov, A. A. 2006. On the eigenvalues of the Sturm-Liouville operator with potentials from Sobolev spaces. Mathematical Notes, Vol. 80, Issue. 5-6, p. 814.
    ×
  • Access

INVERSE SPECTRAL PROBLEMS FOR STURM–LIOUVILLE OPERATORS WITH SINGULAR POTENTIALS. IV. POTENTIALS IN THE SOBOLEV SPACE SCALE

  • Rostyslav O. Hryniv (a1) (a2) and Yaroslav V. Mykytyuk (a1) (a2)
Abstract

We solve the inverse spectral problems for the class of Sturm–Liouville operators with singular real-valued potentials from the Sobolev space $W^{s-1}_2(0,1)$, $s\in[0,1]$. The potential is recovered from two spectra or from one spectrum and the norming constants. Necessary and sufficient conditions for the spectral data to correspond to a potential in $W^{s-1}_2(0,1)$ are established.

    •
      • Send article to Kindle

      To send this article to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle.

      Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

      Find out more about the Kindle Personal Document Service.

      INVERSE SPECTRAL PROBLEMS FOR STURM–LIOUVILLE OPERATORS WITH SINGULAR POTENTIALS. IV. POTENTIALS IN THE SOBOLEV SPACE SCALE
      Available formats
      ×
      Send article to Dropbox

      To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Dropbox.

      INVERSE SPECTRAL PROBLEMS FOR STURM–LIOUVILLE OPERATORS WITH SINGULAR POTENTIALS. IV. POTENTIALS IN THE SOBOLEV SPACE SCALE
      Available formats
      ×
      Send article to Google Drive

      To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Google Drive.

      INVERSE SPECTRAL PROBLEMS FOR STURM–LIOUVILLE OPERATORS WITH SINGULAR POTENTIALS. IV. POTENTIALS IN THE SOBOLEV SPACE SCALE
      Available formats
      ×
Copyright
COPYRIGHT: © Edinburgh Mathematical Society 2006
References
Hide All

p1 Institut für Angewandte Mathematik, Abteilung für Wahrscheinlichkeitstheorie und Mathematische Statistik, Wegelerstraβe 6, D-53115 Bonn, Germany ()

Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Proceedings of the Edinburgh Mathematical Society
  • ISSN: 0013-0915
  • EISSN: 1464-3839
  • URL: /core/journals/proceedings-of-the-edinburgh-mathematical-society
Please enter your name
Please enter a valid email address
Who would you like to send this to? *

CAPTCHA *

Skip to the audio challenge
×

Keywords:

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 120 *
Loading metrics...

Abstract views

Total abstract views: 59 *
Loading metrics...

* Views captured on Cambridge Core between September 2016 - 12th June 2018. This data will be updated every 24 hours.

Cancel
Confirm
×