Some Properties of the Solutions Space of Irregular Elliptic Systems

In this paper we prove Liouville theorem for the irregular nonhomogeneous Cauchy-Riemann equation depended on parameters and we show that qualitative properties of generalized analytic vectors strongly depend on the asymptotic parameters. We give an explicit formula for the solutions of the special type elliptic system of two unknown functions by the spectrum of the corresponding matrix. This result is a revision of the similarity principle for the elliptic system in a whole complex plane.