Аннотация:Using integral transformations, a solution of the initial value problem in a halfplane for a hyperbolic differential-difference equation with a translation in the free term along a spatial variable ranging over the entire real axis is constructed in closed form. We prove that there exists a solution of the problem if the real part of the symbol of the differential-difference operator in the equation is positive. Sufficient conditions on the coefficients and the translation in the equation guaranteeing the existence of a solution of the problem are obtained.
