论文标题
某些非均匀的母系结构域和拾音器插值插值问题
Certain non-homogeneous matricial domains and Pick-Nevanlinna interpolation problem
论文作者
论文摘要
在本文中，我们考虑了某些与复杂平面的给定域自然相关的矩阵域。此类域的一个特定示例是光谱单元球。我们为这些临床域提供了几个结果。我们的第一个结果表明，将光谱单位球的兰斯福德·白人的结果推广，这些临床域的全体形态自动形态群并不具有传统作用。我们还考虑了$ 2 $ - 点和$ 3 $ - 点拾音器 - Nevanlinna插值问题，从设备光盘到这些矩阵域。我们提出的结果为这些问题的全体形态插入剂提供了必要的条件。特别是，我们应该观察到这些结果是巴拉利和钱德尔与这些问题相关的结果的概括。
In this article, we consider certain matricial domains that are naturally associated to a given domain of the complex plane. A particular example of such domains is the spectral unit ball. We present several results for these matricial domains. Our first result shows, generalizing a result of Ransford-White for the spectral unit ball, that the holomorphic automorphism group of these matricial domains does not act transitively. We also consider $2$-point and $3$-point Pick-Nevanlinna interpolation problem from the unit disc to these matricial domains. We present results providing necessary conditions for the existence of a holomorphic interpolant for these problems. In particular, we shall observe that these results are generalizations of the results provided by Bharali and Chandel related to these problems.
