Opuscula Math. 36, no. 3 (2016), 301-314

Opuscula Mathematica

Higher order Nevanlinna functions and the inverse three spectra problem

Olga Boyko
Olga Martinyuk
Vyacheslav Pivovarchik

Abstract. The three spectra problem of recovering the Sturm-Liouville equation by the spectrum of the Dirichlet-Dirichlet boundary value problem on \([0,a]\), the Dirichlet-Dirichlet problem on \([0,a/2]\) and the Neumann-Dirichlet problem on \([a/2,a]\) is considered. Sufficient conditions of solvability and of uniqueness of the solution to such a problem are found.

Keywords: spectrum, eigenvalue, Dirichlet boundary condition, Neumann boundary condition, Marchenko equation, Nevanlinna function.

Mathematics Subject Classification: 34A55, 34B24.

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  • Olga Boyko
  • South-Ukrainian National Pedagogical University, Staroportofrankovskaya 26, Odesa, Ukraine, 65020
  • Olga Martinyuk
  • South-Ukrainian National Pedagogical University, Staroportofrankovskaya 26, Odesa, Ukraine, 65020
  • Vyacheslav Pivovarchik
  • South-Ukrainian National Pedagogical University, Staroportofrankovskaya 26, Odesa, Ukraine, 65020
  • Communicated by P.A. Cojuhari.
  • Received: 2015-10-09.
  • Accepted: 2015-11-16.
  • Published online: 2016-02-21.
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Cite this article as:
Olga Boyko, Olga Martinyuk, Vyacheslav Pivovarchik, Higher order Nevanlinna functions and the inverse three spectra problem, Opuscula Math. 36, no. 3 (2016), 301-314, http://dx.doi.org/10.7494/OpMath.2016.36.3.301

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