Correctness of general boundary-value problems in a half-space for differential equations with constant coefficients in the classes of functions of power growth and decay

We present the necessary and sufficient conditions of correctness of general boundary-value problems in a half-space for homogeneous differential equations with constant coefficients in the spaces of functions that have the exponential behavior at infinity in a separated variable and are rapidly decaying in the remaining variables. On their basis, we obtained the sufficient conditions of solvability of the indicated problems in the spaces of distributions of slow growth.