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Zeroes of the Bergman kernel of Hartogs domains. (English) Zbl 1038.32002

Summary: We exhibit a class of bounded, strongly convex Hartogs domains with real-analytic boundary which are not Lu Qi-Keng, i.e. whose Bergman kernel function has a zero.

MSC:

32A07 Special domains in \({\mathbb C}^n\) (Reinhardt, Hartogs, circular, tube) (MSC2010)
32A25 Integral representations; canonical kernels (Szegő, Bergman, etc.)
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