Riccati equations and Toeplitz-Berezin type symbols on Dirichlet space of unit ball

doi:10.1007/s11464-017-0640-5

Front. Math. China

2017, Vol. 12

Issue (4) : 769-785 https://doi.org/10.1007/s11464-017-0640-5

RESEARCH ARTICLE

Riccati equations and Toeplitz-Berezin type symbols on Dirichlet space of unit ball

Jianjun CHEN^1,⁴, 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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Abstract

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+ XB−CX= 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 Author(s): 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.

URL:

https://academic.hep.com.cn/fmc/EN/10.1007/s11464-017-0640-5
https://academic.hep.com.cn/fmc/EN/Y2017/V12/I4/769

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