A new computation of the Bergman kernel and related techniques

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

Huo, Zhenghui

关键词: Bergman Kernel;    Bergman Projection;    Boundary Behavior;    Generalized Hypergeometric Function;   

Others  :  https://www.ideals.illinois.edu/bitstream/handle/2142/92749/HUO-DISSERTATION-2016.pdf?sequence=1&isAllowed=y

美国|英语

来源: The Illinois Digital Environment for Access to Learning and Scholarship

【 摘 要 】

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.