On Chaotic and Frequently Hypercyclic Properties of Classical Operators in the Weighted Space of Entire Functions

We study the issues of chaoticity and frequently hypercyclicity of various operators in the weighted space of entire functions, defined as the projective limit of Banach spaces. Theorems 4–8 consider the cases of differentiation and shift operators, as well as their compositions in this space. For l...

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Bibliographic Details
Published in:Lobachevskii journal of mathematics Vol. 46; no. 2; pp. 838 - 851
Main Author: Rakhimova, A. I.
Format: Journal Article
Language:English
Published: Moscow Pleiades Publishing 01.02.2025
Springer Nature B.V
Subjects:
Algebra
Analysis
Banach spaces
Commuting
Differentiation
Dynamical systems
Entire functions
Geometry
Mathematical functions
Mathematical Logic and Foundations
Mathematics
Mathematics and Statistics
Operators (mathematics)
Probability Theory and Stochastic Processes
Theorems
weighted space
differentiation operator
shift operator
entire functions
chaotic operator
frequently hypercyclic operator
32C15
ISSN:1995-0802, 1818-9962
Online Access:Get full text
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Summary:We study the issues of chaoticity and frequently hypercyclicity of various operators in the weighted space of entire functions, defined as the projective limit of Banach spaces. Theorems 4–8 consider the cases of differentiation and shift operators, as well as their compositions in this space. For linear continuous operators commuting with differentiation, Theorem 9 shows their chaoticity. In Theorem 10, the frequently hypercyclicity is proved for such operators, and also the most important corollaries of these statements are indicated.
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ISSN:1995-0802
1818-9962
DOI:10.1134/S1995080225600219