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Abstract <p>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.</p>

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

  • 期刊论文

  • 发表日期：

    2025年2月1日

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  • A. I. Rakhimova

摘要

Abstract

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.