On the factorization of several classes of entire functions
The author proves some interesting theorems on factorization of entire functions under composition. For example he proves: Let \[ F(z)=H(z)+\exp (\lambda z+G(z)), \] where both H(z) and G(z) are periodic entire functions with period \(\tau\) and \(\lambda\tau\) /\(\pi\) i is an irrational number. If \(F(z)=f(g)\), where both f and g are non-linear entire functions, then we have the forms of f and g, respectively, \[ f(w)=H_ 1(w)+\exp (cw+H_ 2(w)),\quad g(z)=dz+H_ 3(z), \] where \(dc=\lambda\), both \(H_ 1\) and \(H_ 2\) are periodic functions with period \(d\tau\) and \(H_ 3\) is periodic with period \(\tau\).
scientific article; zbMATH DE number 4034080