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

doi:10.1007/s10473-023-0512-x

摘要/Abstract

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

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

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