Inverse Spectral Problems for Linear Differential Operators and Their Applications

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On an Inverse Spectral Problem for a Convolution Integro-differential Operator (2007, background): “The greatest success in the inverse problem theory has been achieved for the Sturm–Liouville operator (see the historical reviews in [3–5]) and afterwards for differential operators of an arbitrary order (see [1, 7, 8]).”
On inverse spectral problem for non-selfadjoint Sturm–Liouville operator on a finite interval (2007, methodology): “Using the main equation (35) and the method of spectral mappings [10,11] one can also obtain necessary and sufficient conditions for the solvability of the inverse problem similarly to the case of a simple spectrum [7].”