Determination of the diffusion operator on an interval. (English) Zbl 1302.34030

Nabiev, Ibrahim M.

Colloq. Math. 134, No. 2, 165-178 (2014).

The inverse spectral problem is studied for the differential equation \[ y''+(\lambda^2-2\lambda p(x)-q(x))y=0,\; x\in (0,\pi), \] with the boundary conditions \[ y(\pi)=e^{it}y(0),\; y'(\pi)=e^{it}y'(0). \] Sufficient conditions for the solvability of the inverse problem are provided along with an algorithm for the solution.

Reviewer: Vjacheslav Yurko (Saratov)

MSC:

34A55	Inverse problems involving ordinary differential equations
34B24	Sturm-Liouville theory
47E05	General theory of ordinary differential operators (should also be assigned at least one other classification number in Section 47-XX)

Keywords:

differential operators; inverse spectral problems