| 广义Segal-Bargmann空间上无界Toeplitz算子的交换 |
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| 引用本文： | 王晓峰,夏锦,陈建军.广义Segal-Bargmann空间上无界Toeplitz算子的交换[J].数学学报,2019,62(3):409-426. |
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| 作者姓名： | 王晓峰 夏锦 陈建军 |
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| 作者单位： | 1.广州大学数学与信息科学学院 广东高等学校交叉学科实验室 广州 510006;2.肇庆学院数学与统计学院 肇庆 526061;3.中山大学数学学院 广州 510275 |
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| 基金项目： | 国家自然科学基金（11471084；11301101）；广东省青年创新人才项目（2017KQNCX220）；肇庆学院校级课题项目（201732）；肇庆学院博士启动项目（221622） |
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| 摘 要： | 本文给出了复平面C上广义Fock空间中两个Toeplitz算子T_u和T_v的性质.假设u是一个径向函数,两算子是可交换的.在一定的增长条件之下,我们证明出u也是一个径向函数.最后还构造了一个具有本性无界符号的S_p紧,Toeplitz算子.
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| 关 键 词： | Fock空间 交换Toeplitz算子 S_p类 |
Commuting Toeplitz Operators and Toeplitz Operators with Unbounded Symbols on Generalized Segal-Bargmann Space |
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| Xiao Feng WANG,Jin XIA,Jian Jun CHEN.Commuting Toeplitz Operators and Toeplitz Operators with Unbounded Symbols on Generalized Segal-Bargmann Space[J].Acta Mathematica Sinica,2019,62(3):409-426. |
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| Authors: | Xiao Feng WANG Jin XIA Jian Jun CHEN |
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| Institution: | 1.School of Mathematics and Information Science and Key Laboratory of Mathematics, Interdisciplinary Sciences of the Guangdong Higher Education Institute, Guangzhou University, Guangzhou 510006, P. R. China;2.School of Mathematics and Statistics, Zhaoqing University, Zhaoqing 526061, P. R. China;3.School of Mathematics and Computational Science, Sun Yat-sen University, Guangzhou 510275, P. R. China |
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| Abstract: | We consider two Toeplitz operators Tu and Tv on the generalized Fock space over the complex plane C. Let's assume that u is a radial function and the two operators commute. Under certain growth condition at infinity of u and v, we prove that v must be a radial function as well. Finally, we also construct a Sp class of Toeplitz operators on the generalized Fock space with symbols which are essentially unbounded on any point of the complex plane C. |
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| Keywords: | Fock space commuting Toeplitz operator Sp class |
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