scholarly journals Weighted Bergman kernel functions associated to meromorphic functions

2017 ◽  
Vol 47 (1) ◽  
pp. 239-257
Author(s):  
Robert Jacobson
Keyword(s):  
Bergman Kernel ◽  
Meromorphic Functions ◽  
Kernel Functions ◽  
Weighted Bergman Kernel

scholarly journals Gaussian curvature of the Bergman metric with weighted Bergman kernel on the unit disc

2012 ◽  
Vol 45 (3) ◽  
Author(s):  
Marzena Szajewska
Keyword(s):  
Weight Function ◽  
Bergman Kernel ◽  
Gaussian Curvature ◽  
Unit Disc ◽  
Bergman Metric ◽  
Weighted Bergman Kernel

AbstractIn the paper Gaussian curvature of Bergman metric on the unit disc and the dependence of this curvature on the weight function has been studied.

scholarly journals On weights which admit the reproducing kernel of Bergman type

1992 ◽  
Vol 15 (1) ◽  
pp. 1-14 ◽  
Author(s):  
Zbigniew Pasternak-Winiarski
Keyword(s):  
Unit Disk ◽  
Bergman Kernel ◽  
Reproducing Kernel ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Admissible Weight ◽  
Necessary And Sufficient ◽  
Weighted Bergman Kernel

In this paper we consider (1) the weights of integration for which the reproducing kernel of the Bergman type can be defined, i.e., the admissible weights, and (2) the kernels defined by such weights. It is verified that the weighted Bergman kernel has the analogous properties as the classical one. We prove several sufficient conditions and necessary and sufficient conditions for a weight to be an admissible weight. We give also an example of a weight which is not of this class. As a positive example we consider the weightμ(z)=(Imz)2defined on the unit disk inℂ.

Weighted Sub-Bergman Hilbert spaces in the unit ball of ℂn

2020 ◽  
Vol 7 (1) ◽  
pp. 124-132
Author(s):  
Renata Rososzczuk ◽  
Frédéric Symesak
Keyword(s):  
Unit Ball ◽  
Hilbert Spaces ◽  
Bergman Kernel ◽  
Holomorphic Functions ◽  
Sufficient Condition ◽  
Defect Operators ◽  
Weighted Bergman Kernel

AbstractIn this note, we study defect operators in the case of holomorphic functions of the unit ball of ℂn. These operators are built from weighted Bergman kernel with a holomorphic vector. We obtain a description of sub-Hilbert spaces and we give a sufficient condition so that theses spaces are the same.

Sign in / Sign up

Export Citation Format

Share Document