Frontiers of Mathematics in China >

2017 , Vol. 12 >Issue 4: 769 - 785

DOI: 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 WANG , 2 ,
  • Jin XIA 2 ,
  • Guangfu CAO 3
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  • 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

Received date: 31 Oct 2015

Accepted date: 18 Mar 2017

Published date: 06 Jul 2017

Copyright

2017 Higher Education Press and Springer-Verlag Berlin Heidelberg
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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.

Key words： Riccati equation; Toeplitz operator; Dirichlet space; unit ball

Cite this article

Jianjun CHEN , Xiaofeng WANG , Jin XIA , Guangfu CAO . Riccati equations and Toeplitz-Berezin type symbols on Dirichlet space of unit ball[J]. Frontiers of Mathematics in China, 2017 , 12(4) : 769 -785 . DOI: 10.1007/s11464-017-0640-5

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