具有某些调和符号的超循环Bergman-Toeplitz算子
Hypercyclic Bergman-Toeplitz operators with some harmonic symbols
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中文总结 AI 辅助
本文研究Bergman空间上符号为$a\ar{z}+p(z)$的Toeplitz算子的动力学性质，给出了超循环等性质的充要条件，并完整刻画了调和线性多项式符号的情形，还发现同一符号在不同空间上超循环行为可不同。
中文摘要 AI 辅助
本文研究了Bergman空间上符号形如$a \ar{z} + p(z)$的Toeplitz算子的动力学性质，其中$a\ eq 0$且$p$在闭单位圆盘上解析。我们获得了此类算子为超循环、弱混合、混合、混沌或频繁超循环的一些必要条件和充分条件。作为应用，我们得到了具有调和线性多项式符号的Toeplitz算子超循环性的完整刻画。此外，我们证明了具有相同符号的Toeplitz算子在Hardy空间和Bergman空间上可能表现出不同的超循环行为。
英文摘要
Little is known about the dynamics of Toeplitz operators on the Bergman space, and even in the case of harmonic symbols, few results are available. In this paper, we study the dynamical properties of Toeplitz operators with symbols of the form $a \bar{z} + p (z)$ on the Bergman space, where $a\neq 0$ and $p$ is analytic on the closed unit disk. We obtain some necessary conditions and some sufficient conditions for such operators to be hypercyclic, weakly mixing, mixing, chaotic, or frequently hypercyclic. As an application, we obtain a complete characterization of hypercyclicity for Toeplitz operators with harmonic linear polynomial symbols. We also show that Toeplitz operators with the same symbol may exhibit different hypercyclic behavior on the Hardy and Bergman spaces.
发表机构
- Chongqing University（重庆大学）
- Southwest Petroleum University（西南石油大学）
机构由 AI 辅助整理，请以论文原文为准。
