Opuscula Math. 36, no. 3 (2016), 301-314
http://dx.doi.org/10.7494/OpMath.2016.36.3.301

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.
• Accepted: 2015-11-16.
• Published online: 2016-02-21.