| 何莉,曹广福.Segal-Bargmann空间上带无界符号的Toeplitz算子[J].数学研究及应用,2015,35(3):237~255 |
| Segal-Bargmann空间上带无界符号的Toeplitz算子 |
| Toeplitz Operators with Unbounded Symbols on Segal-Bargmann Space |
| 投稿时间：2014-10-10 修订日期：2015-01-16 |
| DOI：10.3770/j.issn:2095-2651.2015.03.001 |
| 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 |
| 基金项目:国家自然科学基金(Grant No.11271092),国家教育部博士点专项基金资助(Grant No.S2011010005367). |
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| 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 $H^{2}(\mathbb{C}^{n},\d V_{\alpha})$. |
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