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. © 2017 Elsevier Inc.
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Citas:
---------- APA ----------
Cardeccia, R. & Muro, S.
(2018)
. Hypercyclic homogeneous polynomials on H(C). Journal of Approximation Theory, 226, 60-72.
http://dx.doi.org/10.1016/j.jat.2017.09.005---------- CHICAGO ----------
Cardeccia, R., Muro, S.
"Hypercyclic homogeneous polynomials on H(C)"
. Journal of Approximation Theory 226
(2018) : 60-72.
http://dx.doi.org/10.1016/j.jat.2017.09.005---------- MLA ----------
Cardeccia, R., Muro, S.
"Hypercyclic homogeneous polynomials on H(C)"
. Journal of Approximation Theory, vol. 226, 2018, pp. 60-72.
http://dx.doi.org/10.1016/j.jat.2017.09.005---------- VANCOUVER ----------
Cardeccia, R., Muro, S. Hypercyclic homogeneous polynomials on H(C). J. Approx. Theory. 2018;226:60-72.
http://dx.doi.org/10.1016/j.jat.2017.09.005