Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8898458 | Journal of Approximation Theory | 2018 | 14 Pages |
Abstract
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(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(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.
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Rodrigo Cardeccia, Santiago Muro,