Chaotic and frequently hypercyclic operators in the weighted space of entire functions
https://doi.org/10.26907/2949-3919.2024.2.84-106
Abstract
We study the issues of chaoticity and frequently hypercyclicity of various operators in the weighted space Fφ(Cn), defined as the projective limit of Banach spaces. Theorems 8–13 consider the cases of differentiation and shift operators, as well as their compositions in Fφ(Cn). For linear continuous operators commuting with differentiation, Theorem 14 shows that they are chaotic in Fφ(Cn). In Theorem 15, such operators are proved to be frequently hypercyclic in Fφ(Cn), and also are the most important consequences of these statements are indicated.
About the Author
A. I. Rakhimova
Subdivision of the Ufa Federal Research Centre of Russian Academy of Science, Ufa Federal Research Centre of Russian Academy of Science
Russian Federation
Alsu Il’darovna Rakhimova
Russian Federation
Alsu Il’darovna Rakhimova
112 Chernyshevsky str., Ufa 450008, Russia
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Review
For citations:
Rakhimova A.I. Chaotic and frequently hypercyclic operators in the weighted space of entire functions. Mathematics and Theoretical Computer Science. 2024;2(2):84-106. (In Russ.) https://doi.org/10.26907/2949-3919.2024.2.84-106
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