Forward and inverse problems for a finite Krein-Stieltjes string. Approximation of constant density by point masses

Abstract

We consider a dynamic inverse problem for a dynamical system which describes the propagation of waves in a Krein string. The problem is reduced to an integral equation and an important special case is considered when the string density is determined by a finite number of point masses distributed over the interval. We derive an equation of Krein type, with the help of which the string density is restored. We also consider 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.