# Wydawnictwa / Czasopisma IMPAN / Annales Polonici Mathematici / Wszystkie zeszyty

## Sequences of differential operators: exponentials, hypercyclicity and equicontinuity

### Tom 77 / 2001

Annales Polonici Mathematici 77 (2001), 169-187 MSC: Primary 47B38; Secondary 30E10, 47A16, 47E05, 47F05. DOI: 10.4064/ap77-2-4

#### Streszczenie

An eigenvalue criterion for hypercyclicity due to the first author is improved. As a consequence, some new sufficient conditions for a sequence of infinite order linear differential operators to be hypercyclic on the space of holomorphic functions on certain domains of ${\mathbb C}^N$ are shown. Moreover, several necessary conditions are furnished. The equicontinuity of a family of operators as above is also studied, and it is characterized if the domain is ${\mathbb C}^N$. The results obtained extend or improve earlier work of several authors.

#### Autorzy

• L. Bernal-GonzálezDepartamento de Análisis Matemático
Avenida Reina Mercedes
41080 Sevilla, Spain
e-mail
• J. A. Prado-TenderoDepartamento de Análisis Matemático