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