The Problem of Determining a Function of the Memory of a Medium and of the Regular Part of a Pulsed Source

Consider the problem of finding two coefficients one of which is under the sign of the integral in the hyperbolic equation and represents the memory of a medium and the other determines the regular part of an impulse source. Additionally, the Fourier transform of the trace of the solution of the direct problem on the hyperplane $y=0$ for two different values of the transformation parameter is given. We establish an estimate of the stability of the solution of the inverse problem under consideration and also the uniqueness theorem.