Necessary and sufficient conditions for the solvability of the inverse problem for non-self-adjoint pencils of Sturm-Liouville operators on the half-line

Abstract

Abstract. Non-self-adjoint Sturm-Liouville differential operators on the half-line with a boundary condition depending polynomially on the spectral parameter are studied. We investigate the inverse problem of recovering the operator from the Weyl function. For this inverse problem we provide necessary and sufficient conditions for its solvability along with a procedure for constructing its solution by the method of spectral mappings.

Determination of differential pencils from dense nodal subset in an interior subinterval

“…Another typical example is related to vibrations of mechanical systems in viscous media; see [21,24,25]. Problems of the form (1.1) have also appeared in the physical literature in the context of scattering of waves and particles (see [10,26] and the references therein).…”