MODEL PROBLEM IN A STRIP FOR THE HYPERBOLIC DIFFERENTIAL-DIFFERENCE EQUATION

The paper investigates the question of the existence of a classical solution to the initial value problem with incomplete initial data on the boundary of the strip for a hyperbolic differential-difference equation. The equation contains a superposition of a differential operator and a translation operator with respect to a spatial variable that varies along the entire real axis. Using the Gelfand–Shilov operational scheme, a solution to the problem was obtained in explicit form.