Hypercyclic Bergman-Toeplitz operators with some harmonic symbols

@misc{leng2026hypercyclic,
  title = {{Hypercyclic Bergman-Toeplitz operators with some harmonic symbols}},
  author = {Qianrui Leng and Xiaoyan Zhang and Xianfeng Zhao},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2609.32650},
  eprint = {2609.32650},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.32650},
  note = {CC0},
}

TY  - UNPB
TI  - Hypercyclic Bergman-Toeplitz operators with some harmonic symbols
AU  - Qianrui Leng
AU  - Xiaoyan Zhang
AU  - Xianfeng Zhao
PY  - 2026
DA  - 2026/10/08
PB  - arXiv
DO  - 10.48550/arxiv.2609.32650
UR  - https://arxiv.org/abs/2609.32650
AB  - 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 z̅ + p (z) on the Bergman space, where a≠ 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.
ER  -