Sequences of differential operators: exponentials, hypercyclicity and equicontinuity
Volume 77 / 2001
Annales Polonici Mathematici 77 (2001), 169-187
MSC: Primary 47B38; Secondary 30E10, 47A16, 47E05, 47F05.
DOI: 10.4064/ap77-2-4
Abstract
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.
