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The Green's Function, the Bergman Kernel and Quadrature Domains in Cn

Electronic Theses of Indian Institute of Science

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Title The Green's Function, the Bergman Kernel and Quadrature Domains in Cn
 
Creator Haridas, Pranav
 
Subject Bargman Span
Green’s Function
Quadrature Domains
Bergman Kernel
Solynin
Sebbar
Mathematics
 
Description In the first part of this thesis, we prove two density theorems for quadrature domains in Cn ,n≥2. It is shown that quadrature domains are dense in the class of all product domains of the form D×Ωwhere D⊂Cn−1 is a smoothly bounded pseudoconvex domain satisfying Bell’s Condition R and Ω⊂Cis a smoothly bounded domain. It is also shown that quadrature domains are dense in the class of all smoothly bounded complete Hartogs domains in C2.
In the second part of this thesis, we study the behaviour of the critical points of the Green’s function when a sequence of domains Dk⊂Rn con-verges to a limiting domain Din the C∞-topology. It is shown that the limit-ing set of the critical points of the Green’s functions Gkfor domains Dk⊂Care the zeroes of the Bergman kernel of D. This generalizes a result of Solynin and Gustafsson, Sebbar.
 
Contributor Verma, Kaushal
 
Date 2018-06-08T07:10:05Z
2018-06-08T07:10:05Z
2018-06-08
2015
 
Type Thesis
 
Identifier http://etd.iisc.ernet.in/2005/3670
http://etd.iisc.ernet.in/abstracts/4540/G27320-Abs.pdf
 
Language en_US
 
Relation G27320