info:eu-repo/semantics/article
Hypercyclic homogeneous polynomials on H(C)
Fecha
2018-02Registro en:
Cardeccia, Rodrigo Alejandro; Muro, Luis Santiago Miguel; Hypercyclic homogeneous polynomials on H(C); Academic Press Inc Elsevier Science; Journal Of Approximation Theory; 226; 2-2018; 60-72
0021-9045
CONICET Digital
CONICET
Autor
Cardeccia, Rodrigo Alejandro
Muro, Luis Santiago Miguel
Resumen
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.