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Weighted generalization of the Ramadanov's theorem and further considerations

Zbigniew Pasternak-Winiarski, Paweł Wójcicki (2018)

Czechoslovak Mathematical Journal

We study the limit behavior of weighted Bergman kernels on a sequence of domains in a complex space ℂ N , and show that under some conditions on domains and weights, weighed Bergman kernels converge uniformly on compact sets. Then we give a weighted generalization of the theorem given by M. Skwarczyński (1980), highlighting some special property of the domains, on which the weighted Bergman kernels converge uniformly. Moreover, we show that convergence of weighted Bergman kernels implies this property,...

Weil's formulae and multiplicity

Maria Frontczak, Andrzej Miodek (1991)

Annales Polonici Mathematici

The integral representation for the multiplicity of an isolated zero of a holomorphic mapping f : ( ℂ n , 0 ) → ( ℂ n , 0 ) by means of Weil’s formulae is obtained.

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 ℂ 2

Jim Arlebrink (1993)

Annales de l'institut Fourier

Let D be a bounded strictly pseudoconvex domain in ℂ 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 ℂ 2 .

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