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

##### 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
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