| Bergman-Hartogs型域的全纯自同构群 |
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| 引用本文： | 潘利双,王安.Bergman-Hartogs型域的全纯自同构群[J].中国科学:数学,2015,45(1):31-42. |
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| 作者姓名： | 潘利双 王安 |
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| 作者单位： | 首都师范大学数学科学学院, 北京 100048 |
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| 基金项目： | 国家自然科学基金(批准号: 11371257) 和北京市自然科学基金(批准号: 1122010) 资助项目 |
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| 摘 要： | 我们考虑一类以有界对称域D为底的Bergman-Hartogs型域Ω={(wm(1),...,w(r),z)∈C1×···×Cmr×D:∥w(1)∥2p1+···+∥w(r)∥2prKD(z,z)-q},其中KD(z,z)是D上的Bergman核函数,r 1且为正整数,参数p1,...,pr1和q0为实数.我们给出它的全纯自同构群,并且证明当r=1时此自同构群为最大全纯自同构群;当r1时,若Ω的全纯自同构变换F将(0,z)∈{0}×D映到(0,z*)∈{0}×D,则F在我们给出的全纯自同构群中.
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| 关 键 词： | Bergman-Hartogs 型域 全纯自同构群 有界对称域 |
The holomorphic automorphism group of the domains of the Bergman-Hartogs type |
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| PAN LiShuang,WANG An.The holomorphic automorphism group of the domains of the Bergman-Hartogs type[J].Scientia Sinica Mathemation,2015,45(1):31-42. |
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| Authors: | PAN LiShuang WANG An |
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| Abstract: | We consider the domain Ω of the Bergman-Hartogs type which bases on any bounded symmetric domain D,
where KD(z, z) denotes the Bergman kernel on D, r is a positive integer, p1, …, pr > 1 and q > 0 are real parameters. We give the holomorphic automorphism group of Ω, and prove that the given holomorphic automorphism group is the full holomorphic automorphism group of Ω for r = 1. In addition, when r > 1, if the holomorphic automorphism mapping F on Ω maps (0, z) ∈ {0} × D to (0, z*) ∈ {0} × D, then F belongs to the given holomorphic automorphism group. |
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| Keywords: | domain of the Bergman-Hartogs type holomorphic automorphism group bounded symmetric domain |
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