Completeness of the system of entire nonnegative powers of analytic functions in $A(D)$

We consider a method for proving the completeness of some systems of analytic functions in the space $A(D)$ for the value of some parameter equal to 3. The method had been previously studied by the author for the value of this parameter equal to 2. We point out some applications of the above results to the Abel–Goncharov problem and the Gel'fond–Ibragimov problem, as well as in other cases.