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 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 . The results obtained extend or improve earlier work of several authors.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ap77-2-4,
author = {L. Bernal-Gonz\'alez and J. A. Prado-Tendero},
title = {Sequences of differential operators: exponentials, hypercyclicity and equicontinuity},
journal = {Annales Polonici Mathematici},
volume = {77},
year = {2001},
pages = {169-187},
zbl = {0990.47031},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap77-2-4}
}
L. Bernal-González; J. A. Prado-Tendero. Sequences of differential operators: exponentials, hypercyclicity and equicontinuity. Annales Polonici Mathematici, Tome 77 (2001) pp. 169-187. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap77-2-4/