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Reconstruction of Nonsplitting Boundary Conditions of the Sturm–Liouville Operator from a Minimal Set of Eigenvalues

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Abstract

We study the inverse spectral problem of reconstructing nonsplitting boundary conditions for the Sturm–Liouville operator from a minimal amount of spectral data. Necessary and sufficient conditions are derived for the existence of solutions of the problem under consideration and for these solutions to be isolated or nonisolated. We propose a simple analytical algorithm for reconstructing boundary conditions. (Explicit formulas are provided for the coefficients of the boundary conditions.) It is shown that the condition determining the properties of the problem is the dimension of the linear span of matrices of fundamental solution systems corresponding to the given spectral data.

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Funding

This work was facilitated by the Moscow Center for Fundamental and Applied Mathematics. The research by Ya.T. Sultanaev and N.F. Valeev was supported by the Russian Foundation for Basic Research, project no. 18-01-00250-a.

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Authors and Affiliations

  1. Lomonosov Moscow State University, Moscow, 119991, Russia

    V. A. Sadovnichii

  2. Akmulla Bashkir State Pedagogical University, Ufa, 450008, Russia

    Ya. T. Sultanaev

  3. Institute of Mathematics with Computing Centre, Subdivision of the Ufa Federal Research Centre, Russian Academy of Science, Ufa, 450008, Russia

    N. F. Valeev

Authors
  1. V. A. Sadovnichii
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  2. Ya. T. Sultanaev
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  3. N. F. Valeev
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Corresponding authors

Correspondence to V. A. Sadovnichii, Ya. T. Sultanaev or N. F. Valeev.

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Translated by V. Potapchouck

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Sadovnichii, V.A., Sultanaev, Y.T. & Valeev, N.F. Reconstruction of Nonsplitting Boundary Conditions of the Sturm–Liouville Operator from a Minimal Set of Eigenvalues. Diff Equat 56, 1290–1297 (2020). https://doi.org/10.1134/S00122661200100055

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  • DOI: https://doi.org/10.1134/S00122661200100055

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