Reconstruction and solvability for discontinuous Hochstadt–Lieberman problems

  • Chuan-Fu Yang

    Nanjing University of Science and Technology, China
  • Natalia P. Bondarenko

    Samara National Research University, Russian Federation
Reconstruction and solvability for discontinuous Hochstadt–Lieberman problems cover

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Abstract

We consider Sturm–Liouville problems with a discontinuity in an interior point, which are motivated by the inverse problems for the torsional modes of the Earth. We assume that the potential on the right half-interval and the coefficient in the right boundary condition are given. Half-inverse problems are studied, that consist in recovering the potential on the left half-interval and the left boundary condition from the eigenvalues. If the discontinuity belongs to the left half-interval, the position and the parameters of the discontinuity also can be reconstructed. In this paper, we provide reconstructing algorithms and prove existence of solutions for the considered inverse problems. Our approach is based on interpolation of entire functions.

Cite this article

Chuan-Fu Yang, Natalia P. Bondarenko, Reconstruction and solvability for discontinuous Hochstadt–Lieberman problems. J. Spectr. Theory 10 (2020), no. 4, pp. 1445–1469

DOI 10.4171/JST/332