An Identification Problem of Memory Function of a Medium and the Form of an Impulse Source

In the paper the problem of identification of two functions, one of which is under the integral sign in a hyperbolic equation and represents the medium's memory, the other one defines the regular part of an impulse source is considered. As additional information Fourier image trace solution of a direct problem on the hyperplane $y=0$ for two different values of transformation parameters is given. The estimate of stability of the solution of the inverse problem and the uniqueness theorems is proved.