赵振刚.$D^2(\Omega,\rho)$的再生核与再生核诱导的度量[J].数学研究及应用,2009,29(4):587~598
$D^2(\Omega,\rho)$的再生核与再生核诱导的度量
Reproducing Kernel for $D^2(\Omega,\rho)$ and Metric Induced by Reproducing Kernel
投稿时间:2007-09-03  修订日期:2008-01-04
DOI:10.3770/j.issn:1000-341X.2009.04.003
中文关键词:  Carath\`eodory体积元素  Eisenmann-kobayashi体积元素  有界对称域.
英文关键词:harmonic Bergman spaces  harmonic Bergman kernels.
基金项目:国家自然科学基金(No.10401024).
作者单位
赵振刚 首都师范大学数学系, 北京 100037 
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中文摘要:
      给出与有界对称域等价的一个充分必要条件.
英文摘要:
      important property of the reproducing kernel of $D^2(\Omega,\rho)$ is obtained and the reproducing kernels for $D^2(\Omega,\rho)$ are calculated when $\Omega=B_n\times B_n$ and $\rho$ are some special functions. A reproducing kernel is used to construct a semi-positive definite matrix and a distance function defined on $\Omega \times\Omega$. An inequality is obtained about the distance function and the pseudo-distance induced by the matrix.
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