Аннотация:The paper studies the question of the existence of classical solutions to a two-dimensional hyperbolic equation in a half-plane containing translation operators in lower derivatives acting with respect to a spatial variable. All translations take arbitrary real values. A multiparameter family of infinitely smooth solutions to the specified equation is constructed in explicit form using an operational scheme. A theorem is proved that the constructed solutions are classical if the real part of the symbol of the differential-difference operator in the equation is positive.
