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Zeroes of the Bergman kernel of Hartogs domains

Miroslav Engliš (2000)

Commentationes Mathematicae Universitatis Carolinae

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.

Zeros of bounded holomorphic functions in strictly pseudoconvex domains in 2

Jim Arlebrink (1993)

Annales de l'institut Fourier

Let D be a bounded strictly pseudoconvex domain in 2 and let X be a positive divisor of D with finite area. We prove that there exists a bounded holomorphic function f such that X is the zero set of f . This result has previously been obtained by Berndtsson in the case where D is the unit ball in 2 .

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