An application of Bergman-Whittaker operator
V. Marić (1974)
Publications de l'Institut Mathématique
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V. Marić (1974)
Publications de l'Institut Mathématique
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Maciej Skwarczyński (1985)
Annales Polonici Mathematici
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M. M. Schiffer (1981)
Annales Polonici Mathematici
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Nowak, Maria (1998)
Annales Academiae Scientiarum Fennicae. Mathematica
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Piotr Jucha (2004)
Studia Mathematica
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We give an equivalent condition for Bergman completeness of Zalcman type domains. This also solves a problem stated by Pflug.
Miroslav Engliš (2000)
Commentationes Mathematicae Universitatis Carolinae
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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.
Friedrich Haslinger (1998)
Annales Polonici Mathematici
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We compute the Bergman kernel functions of the unbounded domains , where . It is also shown that these kernel functions have no zeros in . We use a method from harmonic analysis to reduce the computation of the 2-dimensional case to the problem of finding the kernel function of a weighted space of entire functions in one complex variable.
Nikolai Nikolov, Peter Pflug (2003)
Annales Polonici Mathematici
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Sharp geometrical lower and upper estimates are obtained for the Bergman kernel on the diagonal of a convex domain D ⊂ ℂⁿ which does not contain complex lines. It is also proved that the ratio of the Bergman and Carathéodory metrics of D does not exceed a constant depending only on n.
Philippe Charpentier, Aline Bonami (1990)
Mathematische Zeitschrift
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Ali Abkar, B. Jafarzadeh (2010)
Czechoslovak Mathematical Journal
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We study sub-Bergman Hilbert spaces in the weighted Bergman space . We generalize the results already obtained by Kehe Zhu for the standard Bergman space .
Steven R. Bell (2006)
Studia Mathematica
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Various incarnations of Stefan Bergman's notion of representative coordinates will be given that are useful in a variety of contexts. Bergman wanted his coordinates to map to canonical regions, but they fail to do this for multiply connected regions. We show, however, that it is possible to define generalized Bergman coordinates that map multiply connected domains to quadrature domains which satisfy a long list of desirable properties, making them excellent candidates to be called Bergman...
Bo-Yong Chen (2006)
Studia Mathematica
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Inspired by the work of Engliš, we study the asymptotic behavior of the weighted Bergman kernel together with an application to the Lu Qi-Keng conjecture. Some comparison results between the weighted and the classical Bergman kernel are also obtained.