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D'Angelo, John Laugesen, Richard Tyson, Jeremy Tumanov, Alexander Huo, Zhenghui 2016-11-10T17:50:05Z 2016-11-10T17:50:05Z 2016-07-08 2016-08 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. Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2016-11-09 without embargo terms The student, Zhenghui Huo, accepted the attached license on 2016-07-06 at 12:31. The student, Zhenghui Huo, submitted this Dissertation for approval on 2016-07-06 at 12:42. This Dissertation was approved for publication on 2016-07-08 at 12:14. DSpace SAF Submission Ingestion Package generated from Vireo submission #9748 on 2016-11-09 at 10:22:38 Made available in DSpace on 2016-11-10T17:50:05Z (GMT). No. of bitstreams: 2 HUO-DISSERTATION-2016.pdf: 513858 bytes, checksum: 5b4abc40e302d095605f6508fca0113f (MD5) LICENSE.txt: 4209 bytes, checksum: c67b24b4eac3d43175a7e53ec3b2f3c8 (MD5) Previous issue date: 2016-07-08 application/pdf http://hdl.handle.net/2142/92749 en Copyright 2016 Zhenghui Huo Bergman Kernel Bergman Projection Boundary Behavior Generalized Hypergeometric Function A new computation of the Bergman kernel and related techniques text text Mathematics Mathematics University of Illinois at Urbana-Champaign Dissertation Ph.D.