数学物理学报(英文版) ›› 2023, Vol. 43 ›› Issue (5): 2121-2132.doi: 10.1007/s10473-023-0512-x

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COMPLEX SYMMETRIC $C_0$-SEMIGROUPS ON THE WEIGHTED HARDY SPACES $H_\gamma(\mathbb{D})$*

Xiaohe Hu   

  1. College of Mathematics and Information Science, Henan Normal University, Xinxiang 453007, China
  • 收稿日期:2022-01-16 修回日期:2023-05-03 发布日期:2023-10-25

COMPLEX SYMMETRIC $C_0$-SEMIGROUPS ON THE WEIGHTED HARDY SPACES $H_\gamma(\mathbb{D})$*

Xiaohe Hu   

  1. College of Mathematics and Information Science, Henan Normal University, Xinxiang 453007, China
  • Received:2022-01-16 Revised:2023-05-03 Published:2023-10-25
  • About author:Xiaohe Hu, E-mail: huxiaohe@htu.edu.cn

摘要: In this paper, we study the complex symmetric $C_0$-semigroups of weighted composition operators $W_{\psi, \varphi}$ on the weighted Hardy spaces $H_\gamma$ of the unit disk $\mathbb{D}$. It is well-known that there are only two classes of weighted composition conjugations $\mathcal{A}_{u, v}$ on $H_\gamma(\mathbb{D})$: either $\mathcal{C}_1$ or $\mathcal{C}_2$. We completely characterize $\mathcal{C}_1$-symmetric ($\mathcal{C}_2$-symmetric) $C_0$-semigroups of weighted composition operators $W_{\psi, \varphi}$ on $H_\gamma(\mathbb{D})$.}

关键词: $C_0$-semigroup, complex symmetry, weighted composition operator

Abstract: In this paper, we study the complex symmetric $C_0$-semigroups of weighted composition operators $W_{\psi, \varphi}$ on the weighted Hardy spaces $H_\gamma$ of the unit disk $\mathbb{D}$. It is well-known that there are only two classes of weighted composition conjugations $\mathcal{A}_{u, v}$ on $H_\gamma(\mathbb{D})$: either $\mathcal{C}_1$ or $\mathcal{C}_2$. We completely characterize $\mathcal{C}_1$-symmetric ($\mathcal{C}_2$-symmetric) $C_0$-semigroups of weighted composition operators $W_{\psi, \varphi}$ on $H_\gamma(\mathbb{D})$.}

Key words: $C_0$-semigroup, complex symmetry, weighted composition operator

中图分类号: 

  • 47B33