scholarly journals Duality of Large Fock Spaces in Several Complex Variables and Compact Localization Operators

2021 ◽  
Vol 2021 ◽  
pp. 1-17
Author(s):  
Youqi Liu ◽  
Xiaofeng Wang
Keyword(s):  
Complex Variables ◽  
Several Complex Variables ◽  
Fock Spaces ◽  
Localization Operators ◽  
Dual Spaces ◽  
Algebraic Properties ◽  
Equivalent Conditions

In this paper, dual spaces of large Fock spaces F ϕ p with 0 < p < ∞ are characterized. Also, algebraic properties and equivalent conditions for compactness of weakly localized operators are obtained on F ϕ p 0 < p < ∞ .

scholarly journals Toeplitz operators between large Fock spaces in several complex variables

2021 ◽  
Vol 7 (1) ◽  
pp. 1293-1306
Author(s):  
Ermin Wang ◽  
◽  
Jiajia Xu
Keyword(s):  
Toeplitz Operator ◽  
Toeplitz Operators ◽  
Borel Measure ◽  
Fock Space ◽  
Holomorphic Functions ◽  
Complex Variables ◽  
Several Complex Variables ◽  
Weight Class ◽  
Fock Spaces ◽  
Positive Borel Measure

<abstract><p>Let $ \omega $ belong to the weight class $ \mathcal{W} $, the large Fock space $ \mathcal{F}_{\omega}^{p} $ consists of all holomorphic functions $ f $ on $ \mathbb{C}^{n} $ such that the function $ f(\cdot)\omega(\cdot)^{1/2} $ is in $ L^p(\mathbb{C}^{n}, dv) $. In this paper, given a positive Borel measure $ \mu $ on $ {\mathbb C}^n $, we characterize the boundedness and compactness of Toeplitz operator $ T_\mu $ between two large Fock spaces $ F^{p}_\omega $ and $ F^{q}_\omega $ for all possible $ 0 &lt; p, q &lt; \infty $.</p></abstract>

scholarly journals Meromorphic or Holomorphic Completion of a Reinhardt Domain

1970 ◽  
Vol 38 ◽  
pp. 1-12 ◽  
Author(s):  
Eiichi Sakai
Keyword(s):  
Meromorphic Function ◽  
Power Series ◽  
Meromorphic Functions ◽  
Integral Formula ◽  
Complex Variables ◽  
Several Complex Variables ◽  
Reinhardt Domain ◽  
Continuity Theorem ◽  
Cauchy’S Integral Formula ◽  
Long Time

In the theory of functions of several complex variables, the problem about the continuation of meromorphic functions has not been much investigated for a long time in spite of its importance except the deeper result of the continuity theorem due to E. E. Levi [4] and H. Kneser [3], The difficulty of its investigation is based on the following reasons: we can not use the tools of not only Cauchy’s integral formula but also the power series and there are indetermination points for the meromorphic function of many variables different from one variable. Therefore we shall also follow the Levi and Kneser’s method and seek for the aspect of meromorphic completion of a Reinhardt domain in Cn.

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