Inverse Sturm–Liouville Problem with Spectral Parameter in the Boundary Conditions

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 main results are applied to Hochstadt–Lieberman-type problems polynomial dependence not only conditions but also discontinuity (transmission) inside interval. We prove novel theorems, which generalize improve previous direction. Note that all paper investigated general non-self-adjoint form, method does require simplicity spectrum. Moreover, constructive can be developed future numerical solution solvability stability problems.