Spectral analysis of Volterra integrodifferential equations with the kernels, depending on parameter

Spectral analysis of operator-functions which are the symbols of the abstract integrodifferential equations of the Gurtin-Pipkin is provided. These equations represent abstract wave equations disturbed by terms involving Volterra operators. Correct solvability in the Sobolev space $W_2^2((0,T),A^2)$, for arbitrary $T>0$, of that abstract integrodifferential equations is also studied.