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

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doi:10.1007/s10473-023-0512-x

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

Xiaohe Hu. COMPLEX SYMMETRIC $C_0$ -SEMIGROUPS ON THE WEIGHTED HARDY SPACES $H_\gamma(\mathbb{D})$ ^*[J]. 数学物理学报(英文版), 2023, 43(5): 2121-2132.

Xiaohe Hu. COMPLEX SYMMETRIC $C_0$ -SEMIGROUPS ON THE WEIGHTED HARDY SPACES $H_\gamma(\mathbb{D})$ ^*[J]. Acta mathematica scientia,Series B, 2023, 43(5): 2121-2132.

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