Opuscula Math. 36, no. 3 (), 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

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.