We consider the discrete sets D.cG. of the regions G. in the complex plane and study the subrings of the rings of analytie functions A(G.) corresponding to these discrete sets D. (i=12). Furthermore, we prove that the sets of zeros of the functions which map onto each other under the <?-isomorphism ; A(Gp—>A(Gp, are also mapped onto each other by a eonformal mapping Gj, where ®(/)=/otp.