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Transformation formulas for the Bergman kernels and projections of Reinhardt domains
Author(s):
Siqi
Fu
Journal:
Proc. Amer. Math. Soc.
129
(2001),
1769-1773.
MSC (2000):
Primary 32A25, 32H02
Posted:
November 3, 2000
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Abstract:
Formulas that relate the Bergman kernel and projection of a bounded Reinhardt domain whose closure does not intersect the coordinate planes to those of its covering tube domain are obtained via the Poisson summation formula.
References:
-
- 1.
- Eric Bedford, Proper holomorphic mappings, Bull. Amer. Math. Soc. (NS) 10 (1984), no. 2, 157-175. MR 85b:32041
- 2.
- Steven R. Bell, Proper holomorphic mappings and the Bergman projection, Duke Math. Jour. 48 (1981), no. 1, 167-175. MR 82d:32011
- 3.
- -, The Bergman kernel function and proper holomorphic mappings, Trans. Amer. Math. Soc. 270 (1982), no. 2, 685-691. MR 83i:32033
- 4.
- Harold P. Boas, Siqi Fu, and Emil J. Straube, The Bergman kernel function: explicit formulas and zeroes, Proc. Amer. Math. Soc. 127 (1998), no. 3, 805-811. MR 99f:32037
- 5.
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 , Proper holomorphic mappings: a survey, Several Complex Variables: Proceedings of the Mittag-Leffler Institute, 1987-1988, edited by John Erik Fornæss, Princeton University Press, 1993, pp. 297-363. MR 94a:32042 - 6.
- T. G. Genchev, Paley-Wiener type theorems for functions in Bergman spaces over tube domains, Jour. of Math. Anal. and Appl. 118 (1986), 496-501. MR 87k:32003
- 7.
- Adam Korányi, The Bergman kernel function for tubes over convex cones, Pacific Jour. of Math. 12 (1962), 1355-1359. MR 27:1623
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- 9.
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Additional Information:
Siqi
Fu
Affiliation:
Department of Mathematics, University of Wyoming, Laramie, Wyoming~82071
Email:
sfu@uwyo.edu
DOI:
10.1090/S0002-9939-00-05804-4
PII:
S 0002-9939(00)05804-4
Received by editor(s):
September 10, 1999
Received by editor(s) in revised form:
October 5, 1999
Posted:
November 3, 2000
Communicated by:
Albert Baernstein II
Copyright of article:
Copyright
2000,
American Mathematical Society
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