Sequences of differential operators: exponentials, hypercyclicity and equicontinuity

L. Bernal-González, and J. A. Prado-Tendero. "Sequences of differential operators: exponentials, hypercyclicity and equicontinuity." Annales Polonici Mathematici 77.2 (2001): 169-187. <http://eudml.org/doc/280584>.

@article{L2001,
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 $ℂ^N$ 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 $ℂ^N$. The results obtained extend or improve earlier work of several authors.},
author = {L. Bernal-González, J. A. Prado-Tendero},
journal = {Annales Polonici Mathematici},
keywords = {equicontinuous family; infinite order linear differential operator; subexponential and exponential type; eigenvalue criterion; total subset; Runge domain; polydomain; exponentials; equicontinuity; orbit; hypercyclic; sequences of differential operators},
language = {eng},
number = {2},
pages = {169-187},
title = {Sequences of differential operators: exponentials, hypercyclicity and equicontinuity},
url = {http://eudml.org/doc/280584},
volume = {77},
year = {2001},
}

TY - JOUR
AU - L. Bernal-González
AU - J. A. Prado-Tendero
TI - Sequences of differential operators: exponentials, hypercyclicity and equicontinuity
JO - Annales Polonici Mathematici
PY - 2001
VL - 77
IS - 2
SP - 169
EP - 187
AB - 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 $ℂ^N$ 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 $ℂ^N$. The results obtained extend or improve earlier work of several authors.
LA - eng
KW - equicontinuous family; infinite order linear differential operator; subexponential and exponential type; eigenvalue criterion; total subset; Runge domain; polydomain; exponentials; equicontinuity; orbit; hypercyclic; sequences of differential operators
UR - http://eudml.org/doc/280584
ER -