Theory of Multidimensional Differential Equations in Banach Space and Conditions of Full Solvability

In this paper it is the first time that the theorem of complete solv-ability for non-homogeneous multidimensional differential equation with special operator coefficients in Banach space is established. On proving this theorem it was suddenly discovered that n-dimensional vector space Enx (dimE n x = n) turns into Lie algebra. At that there were obtained new conditions for complete solvability of multidimensional differential equations