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.