Segal-Bargmann空间上带无界符号的Toeplitz算子

Toeplitz Operators with Unbounded Symbols on Segal-Bargmann Space

中文关键词:  Segal-Bargmann空间  Toeplitz算子  无界函数  Schatten类

英文关键词:Segal-Bargmann space  Toeplitz operator  unbounded function  Schatten class

中文摘要:

      本文构造了Segal-Bargmann空间 $H^{2}(\mathbb{C}^{n},dV_{\alpha})$ 上带有 $L^{2}(\mathbb{C}^{n},dV_{\alpha})$ 符号的迹类Toeplitz 算子, 该类特殊符号在 $\mathbb{C}^{n}$ 中任一点的任意领域无界. 此外, 刻画了 $H^{2}(\mathbb{C}^{n},\dV_{\alpha})$ 上具有正测度符号的Toeplitz算子的Schatten $p$性质.

英文摘要:

      In this paper, we construct a function $\varphi$ in $L^{2}(\mathbb{C}^{n},\d V_{\alpha})$ which is unbounded on any neighborhood of each point in $\mathbb{C}^{n}$ such that $T_{\varphi}$ is a trace class operator on the Segal-Bargmann space $H^{2}(\mathbb{C}^{n},\d V_{\alpha})$. In addition, we also characterize the Schatten $p$-class Toeplitz operators with positive measure symbols on $H^{2}(\mathbb{C}^{n},\d V_{\alpha})$.