Classical Solutions of Hyperbolic Equation with Translation Operators in Free Terms

In this paper, we study the question of constructing explicit solutions in a half-space hyperbolic equation containing translation operators space variables all coordinate directions. Such equations are natural generalization classical type, and resulting solution relates value desired function at different points where process takes place. To construct solutions, operating scheme is used, namely, formal application an integral transformation. A theorem proved that constructed if real part symbol differential-difference operator positive. Classes for which condition satisfied given.