有限点的Schwarz-Pick不等式
A finite-Point Schwarz-Pick Inequality
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中文总结 AI 辅助
该研究证明了圆盘全纯自映射的有限点版本Schwarz-Pick不等式，通过比较Bergman Gram矩阵得到精确常数，其取值与点数量及有限Blaschke乘积的映射次数相关。
中文摘要 AI 辅助
我们证明了圆盘全纯自映射的Schwarz-Pick不等式的有限点版本，该估计比较了由若干点及其像构造的Bergman Gram矩阵，其精确常数既依赖于点的数量，也依赖于有限Blaschke乘积的映射次数。
英文摘要
We prove a finite-point version of the Schwarz-Pick inequality for holomorphic self-maps of the disk. The estimate compares Bergman Gram matrices built from several points and their images, and the sharp constant depends on both the number of points and, for finite Blaschke products, the degree of the map. These matrices also arise from the Szegő-kernel metric on the symmetrized polydisc, where the estimate becomes a sharp Schwarz-Pick inequality for the induced holomorphic maps.
