A Classical Solution to a Hyperbolic Differential-Difference Equation with a Translation by an Arbitrary Vector

Abstract: Using an operational scheme, a three-parameter family of solutions is constructed in a half-space for a multidimensional hyperbolic differential-difference equation with translation operators of the general type acting on all spatial variables. The theorem is proved stating that the obtained solutions are classical, provided that the real part of the symbol of the differential-difference operator is positive. Classes of equations are given for which the indicated condition is satisfied. © 2023, Allerton Press, Inc.