Abstract
The three-spectral inverse problem for a Stieltjes string (a thread bearing finite number of point masses) is solved. The inverse problem for a Stieltjes string damped at an interior point with the ends fixed appears to be closely connected to the corresponding three-spectral problem. Conditions obtained are necessary and sufficient for a set of complex numbers to be the spectrum of a Stieltjes string damped at an interior point.
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