Complex Symmetric Toeplitz Operators on the Unit Polydisk and the Unit Ball

2019 ◽  
Vol 40 (1) ◽  
pp. 35-44 ◽  
Author(s):  
Cao Jiang ◽  
Xingtang Dong ◽  
Zehua Zhou
Keyword(s):  
Unit Ball ◽  
Toeplitz Operators ◽  
Unit Polydisk ◽  
Complex Symmetric

Complex symmetric monomial Toeplitz operators on the unit ball

2020 ◽  
Vol 492 (2) ◽  
pp. 124490
Author(s):  
Xiao-He Hu ◽  
Xing-Tang Dong ◽  
Ze-Hua Zhou
Keyword(s):  
Unit Ball ◽  
Toeplitz Operators ◽  
Complex Symmetric

Complex Symmetric Toeplitz Operators

2021 ◽  
Vol 93 (2) ◽  
Author(s):  
Qinggang Bu ◽  
Yong Chen ◽  
Sen Zhu
Keyword(s):  
Toeplitz Operators ◽  
Complex Symmetric

scholarly journals On the Fekete and Szegö Problem for the Class of Starlike Mappings in Several Complex Variables

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Qing-Hua Xu ◽  
Tai-Shun Liu
Keyword(s):  
Banach Space ◽  
Unit Ball ◽  
Unit Disk ◽  
Univalent Functions ◽  
Complex Banach Space ◽  
Complex Variables ◽  
Several Complex Variables ◽  
Unit Polydisk ◽  
Starlike Mappings

LetSbe the familiar class of normalized univalent functions in the unit disk. Fekete and Szegö proved the well-known resultmaxf∈S⁡a3-λa22=1+2e-2λ/(1-λ)forλ∈0, 1. We investigate the corresponding problem for the class of starlike mappings defined on the unit ball in a complex Banach space or on the unit polydisk inCn, which satisfies a certain condition.

scholarly journals Properties of Commutativity of Dual Toeplitz Operators on the Orthogonal Complement of Pluriharmonic Dirichlet Space over the Ball

2016 ◽  
Vol 2016 ◽  
pp. 1-9
Author(s):  
Yinyin Hu ◽  
Yufeng Lu ◽  
Tao Yu
Keyword(s):  
Sobolev Space ◽  
Unit Ball ◽  
Toeplitz Operators ◽  
Dirichlet Space ◽  
Orthogonal Complement ◽  
Pluriharmonic Functions

We completely characterize the pluriharmonic symbols for (semi)commuting dual Toeplitz operators on the orthogonal complement of the pluriharmonic Dirichlet space in Sobolev space of the unit ball. We show that, forfandgpluriharmonic functions,SfSg=SgSfon(Dh)⊥if and only iffandgsatisfy one of the following conditions:(1)bothfandgare holomorphic;(2)bothf¯andg¯are holomorphic;(3)there are constantsαandβ, both not being zero, such thatαf+βgis constant.

scholarly journals Compact Toeplitz operators on weighted harmonic Bergman spaces

1998 ◽  
Vol 64 (1) ◽  
pp. 136-148 ◽  
Author(s):  
Karel Stroethoff
Keyword(s):  
Unit Ball ◽  
Harmonic Functions ◽  
Toeplitz Operators ◽  
Bergman Spaces ◽  
Harmonic Bergman Spaces

AbstractWe consider the Bergman spaces consisting of harmonic functions on the unit ball in Rn that are squareintegrable with respect to radial weights. We will describe compactness for certain classes of Toeplitz operators on these harmonic Bergman spaces.

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