On the factorization of a certain class of entire functions (Q1860729)

Let \(P,Q\) be nonconstant polynomials, \(h\) a periodic entire function with period \(2\pi\) and of order one, \(\alpha\) a transcendental entire function such that the set of singularities of the inverse of \(\alpha\) is bounded, \(G(z)=P(h(\alpha(z)))\) and \(F(z)=G^n(z)+Q(z)\), where \(G^n\) denotes the \(n\)th iterate of \(G\). It is shown that if an entire function \(g\) is a right factor of \(F\) under composition which means that \(F(z)=f(g(z))\) for some nonlinear entire function \(f\), then \(g\) is a common right factor of \(\alpha\) and \(Q\).