广义Segal-Bargmann空间上无界Toeplitz算子的交换
Commuting Toeplitz Operators and Toeplitz Operators with Unbounded Symbols on Generalized Segal-Bargmann Space
本文给出了复平面C上广义Fock空间中两个Toeplitz算子Tu和Tv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.
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.
Fock空间 / 交换Toeplitz算子 / Sp类 {{custom_keyword}} /
Fock space / commuting Toeplitz operator / Sp class {{custom_keyword}} /
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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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