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

Approximation of constant density by point masses. Inverse dynamic problem for dynamical system describing propagation of waves in a Krein string is considered. The forward initial-boundary value problem for this system is reduced to the integral equation. Then the important special case when the density of a string is defined by point masses distributed on a finite interval is studied. Krein type equations are derived, which can be used for recovering of unknown density. The problem of the approximation of constant density by point masses uniformly distributed on the interval and the effect of appearing of a finite speed of wave propagation in the dynamical system is discussed.