University of Illinois Urbana-Champaign

A new computation of the Bergman kernel and related techniques

Huo, Zhenghui

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https://hdl.handle.net/2142/92749

Description

Title
A new computation of the Bergman kernel and related techniques
Author(s)
Huo, Zhenghui
Issue Date
2016-07-08
Director of Research (if dissertation) or Advisor (if thesis)
D'Angelo, John
Doctoral Committee Chair(s)
Laugesen, Richard
Committee Member(s)
  • Tyson, Jeremy
  • Tumanov, Alexander
Department of Study
Mathematics
Discipline
Mathematics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
  • Bergman Kernel
  • Bergman Projection
  • Boundary Behavior
  • Generalized Hypergeometric Function
Abstract
We introduce a technique for obtaining the Bergman kernel on certain Hartogs domains. To do so, we apply a differential operator to a known kernel function on a domain in lower dimensional space. We rediscover some known results and we obtain new explicit formulas. Using these formulas, we analyze the boundary behavior of the kernel function on the diagonal. Our technique also leads us to results about a cancellation of singularities for generalized hypergeometric functions and weighted Bergman kernels. Finally, we give an alternative approach to obtain explicit bases for complex harmonic homogeneous polynomial spaces.
Graduation Semester
2016-08
Type of Resource
text
Permalink
http://hdl.handle.net/2142/92749
Copyright and License Information
Copyright 2016 Zhenghui Huo

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