Model Problem in a Strip for a Hyperbolic Differential-DifferenceEquation

The paper studies the existence of a classical solution of an initial value problem with incomplete initial data on the boundary of a strip for a hyperbolic differential-difference equation. The equation contains a superposition of a differential operator and a translation operator with respect to the spatial variable, which varies along the entire real axis. Using the Gelfand–Shilov operational scheme, we obtain the solution of this problem in closed form.