Classical Solutions of a Multidimensional Hyperbolic Differential–Difference Equation with Shifts of Various Directions in the Potentials

We study the existence of smooth solutions of a multidimensional hyperbolic equation containing the sum of differential operators and shift operators along arbitrary spatial coordinate directions. For this equation, we construct a three-parameter family of solutions. It is proved that the resulting solutions are classical under the condition that the real part of the symbol of the differential–difference operator in the equation is positive. Classes of equations for which this condition holds are given.