Interdependent Components of Generating Systems in the Theory of Pseudo-Holomorphic Functions

1.1. L. Bers [1-3] pointed out that the solutions of the homogeneous Vekua equation w5 aw btii = O[9], by virtue of a fixed chosen generating system, say E := (F, G), accomplishing Im (PG) > 0 in some domain D0 C C and F, G E Hj30 (Holder-continuously differentiable there) is uniquely representable by w(z) = F(z)W(z) + G(z)(z) wherein ço and 0 are real-valued functions in D C D0 . Analogous to the classical theory we establish the differential operator dE/dz : w is called complex differentiable modulo E at z0 E D if there w(z) is complex linear approximable modulo E, i.e. if