We consider a regular indefinite Sturm-Liouville problem with two self-adjoint boundary conditions, one being affinely dependent on the eigen-parameter. We give sufficient conditions under which a basis of each root subspace for this Sturm-Liouville problem can be selected so that the union of all these bases constitutes a Riesz basis of a corresponding weighted Hilbert space.

In this paper, for the first time, we study inverse Sturm–Liouville problem with polynomials of spectral parameter in boundary condition and entire analytic functions second one. For investigation new problem, develop an approach based on construction a special vector functional sequence suitable Hilbert space. The uniqueness recovering potential from part spectrum is proved. Furthermore, our m...