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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

The Bergman kernel function:
Explicit formulas and zeroes


Authors: Harold P. Boas, Siqi Fu and Emil J. Straube
Journal: Proc. Amer. Math. Soc. 127 (1999), 805-811
MSC (1991): Primary 32H10
MathSciNet review: 1469401
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Abstract: We show how to compute the Bergman kernel functions of some special domains in a simple way. As an application of the explicit formulas, we show that the Bergman kernel functions of some convex domains, for instance the domain in \begin{math}\mathbb{C}^3\end{math} defined by the inequality \begin{math}|z_1|+|z_2|+|z_3|<1\end{math}, have zeroes.


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Additional Information

Harold P. Boas
Affiliation: Department of Mathematics, Texas A&M University, College Station, Texas 77843–3368
Email: boas@math.tamu.edu

Siqi Fu
Affiliation: Department of Mathematics, Texas A&M University, College Station, Texas 77843–3368
Address at time of publication: Department of Mathematics, University of Wyoming, Laramie, Wyoming 82071-3036
Email: sfu@math.tamu.edu

Emil J. Straube
Affiliation: Department of Mathematics, Texas A&M University, College Station, Texas 77843–3368
Email: straube@math.tamu.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-99-04570-0
PII: S 0002-9939(99)04570-0
Received by editor(s): June 30, 1997
Additional Notes: This research was supported in part by NSF grant number DMS 9500916.
Communicated by: Steven R. Bell
Article copyright: © Copyright 1999 American Mathematical Society