New formulas of the Bergman kernels for complex ellipsoids in $\mathbb {C}^2$
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Abstract:
We compute the explicit formula of the Bergman kernel for a nonhomogeneous domain $\{(z_1,z_2)\in \mathbb {C}^2:|z_1|^{4/q_1}+|z_2|^{4/q_2}<1\}$ for any positive integers $q_1$ and $q_2$. We also prove that among the domains $D_p:=\{(z_1,z_2)\in \mathbb {C}^2:|z_1|^{2p_1}+|z_2|^{2p_2}<1\}$ in $\mathbb {C}^2$ with $p=(p_1,p_2)\in \mathbb {N}^2$, the Bergman kernel is represented in terms of closed forms if and only if $p=(p_1,1),(1,p_2)$, or $p=(2,2)$.References
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Additional Information
- Jong-Do Park
- Affiliation: Department of Mathematical Sciences, Seoul National University, Seoul 151-747, Korea
- Address at time of publication: Department of Mathematics, Pohang University of Science and Technology, San 31, Hyoja-dong, Namgu, Pohang, Kyungbuk, 790-784, Korea
- Email: jongdopark@gmail.com, jdpark@postech.ac.kr
- Received by editor(s): February 28, 2007
- Published electronically: July 15, 2008
- Additional Notes: The author was supported by Korea Research Foundation Grant 2005-070-C00007 and partially supported by BK21 CoDiMaRO
- Communicated by: Mei-Chi Shaw
- © Copyright 2008
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 136 (2008), 4211-4221
- MSC (2000): Primary 32A25; Secondary 33D70
- DOI: https://doi.org/10.1090/S0002-9939-08-09576-2
- MathSciNet review: 2431034