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Title:A new computation of the Bergman kernel and related techniques
Author(s):Huo, Zhenghui
Director of Research:D'Angelo, John
Doctoral Committee Chair(s):Laugesen, Richard
Doctoral Committee Member(s):Tyson, Jeremy; Tumanov, Alexander
Department / Program:Mathematics
Degree Granting Institution:University of Illinois at Urbana-Champaign
Subject(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.
Issue Date:2016-07-08
Rights Information:Copyright 2016 Zhenghui Huo
Date Available in IDEALS:2016-11-10
Date Deposited:2016-08

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