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广义Segal-Bargmann空间上无界Toeplitz算子的交换

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广义Segal-Bargmann空间上无界Toeplitz算子的交换 王晓峰1, 夏锦1, 陈建军2,31 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 Commuting Toeplitz Operators and Toeplitz Operators with Unbounded Symbols on Generalized Segal-Bargmann Space Xiao Feng WANG1, Jin XIA1, Jian Jun CHEN2,31 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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摘要本文给出了复平面C上广义Fock空间中两个Toeplitz算子TuTv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v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Sp紧Toeplitz算子.
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收稿日期: 2018-08-13
MR (2010):O174.5
基金资助: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)
通讯作者:陈建军E-mail: chenarmy@foxmail.com
作者简介: 王晓峰,E-mail:wxf@gzhu.edu.cn;夏锦,E-mail:xiaj@cdut.edu.cn
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. Xiao Feng WANG, Jin XIA, Jian Jun CHEN. Commuting Toeplitz Operators and Toeplitz Operators with Unbounded Symbols on Generalized Segal-Bargmann Space. Acta Mathematica Sinica, Chinese Series, 2019, 62(3): 409-426.
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http://www.actamath.com/Jwk_sxxb_cn/CN/ http://www.actamath.com/Jwk_sxxb_cn/CN/Y2019/V62/I3/409


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[1]王晓峰, 夏锦, 陈建军. 广义Fock空间上的Hankel算子[J]. 数学学报, 2019, 62(4): 561-572.
[2]曹广福, 王晓峰, 何莉. 解析Sobolev型空间上的算子与算子代数[J]. 数学学报, 2017, 60(1): 69-80.



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