Classical Solutions of One Multidimensional HyperbolicEquation with Incommensurable Translationsin Lower Derivatives

The paper studies the question of the existence of classical solutions in the half-space to a multidimensional hyperbolic differential-difference equation containing translation operators with respect to spatial variables in lower derivatives. It proves a theorem that solutions constructed using integral transformations in explicit form are classical if the real part of the symbol of the differential-difference operator in the equation is positive.