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Frontiers of Mathematics in China

Front. Math. China    2017, Vol. 12 Issue (4) : 769-785     DOI: 10.1007/s11464-017-0640-5
Riccati equations and Toeplitz-Berezin type symbols on Dirichlet space of unit ball
Jianjun CHEN1,4, Xiaofeng WANG2(), Jin XIA2, Guangfu CAO3
1. School of Mathematics and Statistics, Zhaoqing University, Zhaoqing 526061, China
2. School of Mathematics and Information Science and Key Laboratory of Mathematics and Interdisciplinary Sciences of the Guangdong Higher Education Institute, Guangzhou University, Guangzhou 510006, China
3. College of Mathematics and Informatics, South China Agricultural University, Guangzhou 510642, China
4. School of Mathematics and Computational Science, Sun Yat-sen University, Guangzhou 510275, China
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The present paper mainly gives some applications of Berezin type symbols on the Dirichlet space of unit ball. We study the solvability of some Riccati operator equations of the form XAX+ XBCX= Drelated to harmonic Toeplitz operators on the Dirichlet space. Especially, the invariant subspaces of Toeplitz operators are also considered.

Keywords Riccati equation      Toeplitz operator      Dirichlet space      unit ball     
Corresponding Authors: Xiaofeng WANG   
Issue Date: 06 July 2017
 Cite this article:   
Jianjun CHEN,Xiaofeng WANG,Jin XIA, et al. Riccati equations and Toeplitz-Berezin type symbols on Dirichlet space of unit ball[J]. Front. Math. China, 2017, 12(4): 769-785.
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Jianjun CHEN
Xiaofeng WANG
Guangfu CAO
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