2017/03/14 by Cardeccia, Rodrigo, Muro, Santiago
#30D20 #30K99 #37F10 #47A16 #47H60 #FOS: Mathematics #Functional Analysis (math.FA)
paper · doi:10.48550/arxiv.1703.04773
It is known that homogeneous polynomials on Banach spaces cannot be hypercyclic, but there are examples of hypercyclic homogeneous polynomials on some non-normable Fréchet spaces. We show the existence of hypercyclic polynomials on H(\mathbb C), by exhibiting a concrete polynomial which is also the first example of a frequently hypercyclic homogeneous polynomial on any F-space. We prove that the homogeneous polynomial on H(\mathbb C) defined as the product of a translation operator and the evaluation at 0 is mixing, frequently hypercyclic and chaotic. We prove, in contrast, that some natural related polynomials fail to be hypercyclic.