复合运算符的Kitai准则

IF 1.2 3区数学 Q1 MATHEMATICS

Journal of Mathematical Analysis and Applications Pub Date : 2025-02-10 DOI:10.1016/j.jmaa.2025.129347

Daniel Gomes , Karl-G. Grosse-Erdmann

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引用次数: 0

摘要

我们提出了一个通用的、自然的框架来研究可测函数空间上复合算子的动力学，在这个框架中，我们重新考虑了Bayart、Darji和Pires在2018年获得的超循环和混合复合算子的特征。我们证明了超循环和弱混合的概念在这种情况下是一致的，如果系统是耗散的，循环复合算符与超循环算符一致。给出了满足基泰准则的可逆复合算子的一个刻画，并构造了一个不满足基泰准则的混合复合算子的例子。对于具有有界畸变的可逆耗散系统，我们证明了满足基泰准则的复合算子与混合算子重合。

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Kitai's Criterion for composition operators

We present a general and natural framework to study the dynamics of composition operators on spaces of measurable functions, in which we then reconsider the characterizations for hypercyclic and mixing composition operators obtained by Bayart, Darji and Pires in 2018. We show that the notions of hypercyclicity and weak mixing coincide in this context and, if the system is dissipative, the recurrent composition operators agree with the hypercyclic ones. We also give a characterization for invertible composition operators satisfying Kitai's Criterion, and we construct an example of a mixing composition operator not satisfying Kitai's Criterion. For invertible dissipative systems with bounded distortion we show that composition operators satisfying Kitai's Criterion coincide with the mixing operators.

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来源期刊

Journal of Mathematical Analysis and Applications 数学-数学

CiteScore

2.50

自引率

7.70%

发文量

790

审稿时长

6 months

期刊介绍： The Journal of Mathematical Analysis and Applications presents papers that treat mathematical analysis and its numerous applications. The journal emphasizes articles devoted to the mathematical treatment of questions arising in physics, chemistry, biology, and engineering, particularly those that stress analytical aspects and novel problems and their solutions. Papers are sought which employ one or more of the following areas of classical analysis: • Analytic number theory • Functional analysis and operator theory • Real and harmonic analysis • Complex analysis • Numerical analysis • Applied mathematics • Partial differential equations • Dynamical systems • Control and Optimization • Probability • Mathematical biology • Combinatorics • Mathematical physics.