Linear factorization of hypercyclic functions for differential operators

Abstract

On the Fréchet space of entire functions H(C), we show that every nonscalar continuous linear operator L:H(C)→H(C) which commutes with differentiation has a hypercyclic vector f(z) in the form of the infinite product of linear polynomials:f(z)=∏j=1∞(1−zaj), where each aj is a nonzero complex number.