谱球和对称多圆盘的格林函数
Green functions of the spectral ball and symmetrized polydisk
摘要：
谱球的格林函数在等谱簇上是常数，永远不会小于对称化多圆盘上对应物的拉回，并且在极点是循环（非减损）矩阵的一般情况下等于它。当极点是贬损的时，不等式总是严格的，两个函数之间的差取决于极点的若尔当分解中出现的严格上三角块的零阶。特别是，光谱球的格林函数在其参数上是不对称的。此外，还对对称化多圆盘中的不变函数给出了一些估计，例如Carathéodory距离和格林函数的（无穷小版本），表明它们在大于或等于$3$的维度上是不同的。
英文摘要：
The Green function of the spectral ball is constant over the isospectral varieties, is never less than the pullback of its counterpart on the symmetrized polydisk, and is equal to it in the generic case where the pole is a cyclic (non-derogatory) matrix. When the pole is derogatory, the inequality is always strict, and the difference between the two functions depends on the order of nilpotence of the strictly upper triangular blocks that appear in the Jordan decomposition of the pole. In particular, the Green function of the spectral ball is not symmetric in its arguments. Additionally, some estimates are given for invariant functions in the symmetrized polydisc, e.g. (infinitesimal versions of) the Carathéodory distance and the Green function, that show that they are distinct in dimension greater or equal to $3$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
