发表机构
Indian Institute of Technology Bombay（印度理工学院孟买分校）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究针对有限维单位球中的单项式簇建立几何刚性定理，推导得到完全Nevanlinna-Pick狄利克雷级数核乘子代数及有界Reinhardt域上相关核的等距分类结果。
AI 中文摘要
我们针对有限维单位球中的一类单项式簇建立了几何刚性定理：将这类簇中的一个映射到另一个的每个球自同构都是酉的，且当这类等价关系存在时，也可通过环境坐标的置换实现。由此，我们基于定义权重和频率数据，得到了整生成完全Nevanlinna-Pick狄利克雷级数核的乘子代数的完整等距分类；还得到了有界Reinhardt域上一类完全Nevanlinna-Pick核的显式等距分类。
英文摘要
We establish a geometric rigidity theorem for a class of monomial varieties in finite-dimensional unit balls. Every ball automorphism mapping one such variety onto another is unitary, and whenever such an equivalence exists, it can also be realized by a permutation of the ambient coordinates. As a consequence, we obtain a complete isometric classification of the multiplier algebras of integrally generated complete Nevanlinna--Pick Dirichlet series kernels in terms of their defining weight and frequency data. We also obtain an explicit isometric classification for a class of complete Nevanlinna--Pick kernels on bounded Reinhardt domains.
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