Geodesic
Sequences of differential operators: exponentials, hypercyclicity and equicontinuity
L. Bernal-González1 ; J. A. Prado-Tendero1
1Departamento de Análisis Matemático Facultad de Matemáticas, Apdo. 1160 Avenida Reina Mercedes 41080 Sevilla, Spain
Annales Polonici Mathematici, Tome 77 (2001) no. 2, pp. 169-187
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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.
DOI : 10.4064/ap77-2-4
Keywords: eigenvalue criterion hypercyclicity due first author improved consequence sufficient conditions sequence infinite order linear differential operators hypercyclic space holomorphic functions certain domains mathbb shown moreover several necessary conditions furnished equicontinuity family operators above studied characterized domain mathbb results obtained extend improve earlier work several authors

L. Bernal-González  1   ; J. A. Prado-Tendero  1

1 Departamento de Análisis Matemático Facultad de Matemáticas, Apdo. 1160 Avenida Reina Mercedes 41080 Sevilla, Spain 
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L. Bernal-González; J. A. Prado-Tendero. Sequences of differential operators: exponentials,
hypercyclicity and equicontinuity. Annales Polonici Mathematici, Tome 77 (2001) no. 2, pp. 169-187. doi: 10.4064/ap77-2-4

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