Classical solutions of hyperbolic differential-difference equation with shift by an arbitrary vector

We construct three-parameter family of solutions in a half-space for the multidimensional hyperbolic differential-difference equation with shift operators of the general type acting on all spatial variables. Solutions are built using an operating scheme. We prove the theorem stating that these solutions are classical under the condition that the real part of the symbol of the differential-difference operator is positive. Classes of equations for which the indicated condition is satisfied are given.