Toeplitz Operators with Unbounded Symbols on Segal-Bargmann Space
Received:October 10, 2014  Revised:January 16, 2015
Key Words: Segal-Bargmann space   Toeplitz operator   unbounded function   Schatten class  
Fund Project:Supported by the National Natural Science Foundation of China (Grant No.11271092) and the Natural Science Foundation of Guangdong Province (Grant No.S2011010005367).
Author NameAffiliation
Li HE Department of Mathematics, Guangzhou University, Guangdong 510006, P. R. China 
Guangfu CAO 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 $H^{2}(\mathbb{C}^{n},\d V_{\alpha})$.
Citation:
DOI:10.3770/j.issn:2095-2651.2015.03.001
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