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We present the complete version including proofs of the results announced in [1]. Namely, for the problem of small transversal vibrations of a damped string of nonuniform stiffness with one end fixed we give the description of the spectrum and solve the inverse problem: find the conditions which should be satisfied by a sequence of complex numbers to be the spectrum of a damped string.

Обратная задача Штурма - Лиувилля с зависящими от спектрального параметра краевыми условиями