| Segal-Bargmann空间上带无界符号的Toeplitz算子 |
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| 引用本文： | 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 |
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| 作者姓名： | 何莉 曹广福 |
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| 作者单位： | 广州大学数学与信息科学学院, 广东 广州 510006;广州大学数学与信息科学学院, 广东 广州 510006 |
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| 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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| 摘 要： | In this paper,we construct a function φ in L2(Cn,d Vα) which is unbounded on any neighborhood of each point in Cnsuch that Tφ is a trace class operator on the SegalBargmann space H2(Cn,d Vα).In addition,we also characterize the Schatten p-class Toeplitz operators with positive measure symbols on H2(Cn,d Vα).
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| 关 键 词： | Segal-Bargmann space Toeplitz operator unbounded function Schatten class |
| 收稿时间： | 2014-10-10 |
| 修稿时间： | 2015-01-16 |
Toeplitz Operators with Unbounded Symbols on Segal-Bargmann Space |
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| Li HE and Guangfu CAO. Toeplitz Operators with Unbounded Symbols on Segal-Bargmann Space[J]. Journal of Mathematical Research with Applications, 2015, 35(3): 237-255 |
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| Authors: | Li HE and Guangfu CAO |
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| Affiliation: | Department of Mathematics, Guangzhou University, Guangdong 510006, P. R. China;Department of Mathematics, Guangzhou University, Guangdong 510006, P. R. China |
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| Abstract: | 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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| Keywords: | Segal-Bargmann space Toeplitz operator unbounded function Schatten class |
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