Forward and Inverse Problems for a Finite Krein–Stieltjes String. Approximation of Constant Density by Point Masses

A dynamic inverse problem for a dynamical system that describes the propagation of waves in a Krein string is considered. The problem is reduced to an integral equation, and an important special case is considered where the string density is determined by a finite number of point masses distributed over the interval. An equation of Krein type, with the help of which the string density is restored, is derived. The approximation of constant density by point masses uniformly distributed over the interval and the effect of the appearance of a finite wave propagation velocity in the dynamical system are also studied.