A new computation of the Bergman kernel and related techniques

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.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Mathematics

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2016

Author dc:creator

• Huo, Zhenghui

Contributors dc:contributor

• D'Angelo, John
• Laugesen, Richard
• Tyson, Jeremy
• Tumanov, Alexander

• Bergman Kernel
• Bergman Projection
• Boundary Behavior
• Generalized Hypergeometric Function

Statement dc:rights

• Copyright 2016 Zhenghui Huo

Language dc:language

en

Handle dc:identifier

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

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/92749