Hilbert spaces of holomorphic functions, the Bergman kernel, and biholomorphic mappings

2006 ◽  
pp. 413-446
Author(s):  
Robert Greene ◽  
Steven Krantz
Keyword(s):  
Hilbert Spaces ◽  
Bergman Kernel ◽  
Holomorphic Functions ◽  
Spaces Of Holomorphic Functions

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.

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