论文标题
非交通性的免费通用单片，pluriharmonic con轭和多重性单曲
Noncommutative free universal monodromy, pluriharmonic conjugates, and plurisubharmonicity
论文作者
论文摘要
我们表明，单肌定理符合非交通性的自由分析函数的任意连接的免费集合。应用是众多的 - pluriharmonic的自由功能具有全球定义的多元偶联物，局部可逆功能是全球可逆的，并且在连接的免费集合上的分析延续中没有非平凡的共同体学理论。我们描述了为什么面包板 - 贝尔 - 霍斯多夫公式在单片上具有有限的收敛半径，并解决了马丁·桑莫维奇的相关问题。我们概括了Dym-Helton-Klep-McCullough-volcic定理 - 当且只有可以将其写入具有分析函数的凸函数的组成时，只有将其作为凸函数的组成时，一个均匀的无分析性非交通函数才是多元性的。分解本质上是独一无二的。结果首先是在本地建立的，然后自由通用单构型意味着全球结果。此外，我们看到plurisubharmonicity是一种几何特性 - 在整个领域上，邻域上的真实分析自由函数Plurisubharmonic在邻域上都是plurisubharmonic。我们提供了一个分析性的绿色liouville定理，整个免费的多元式功能是遗传性和反遗传性正方形的总和。
We show that the monodromy theorem holds on arbitrary connected free sets for noncommutative free analytic functions. Applications are numerous-- pluriharmonic free functions have globally defined pluriharmonic conjugates, locally invertible functions are globally invertible, and there is no nontrivial cohomology theory arising from analytic continuation on connected free sets. We describe why the Baker-Campbell-Hausdorff formula has finite radius of convergence in terms of monodromy, and solve a related problem of Martin-Shamovich. We generalize the Dym-Helton-Klep-McCullough-Volcic theorem-- a uniformly real analytic free noncommutative function is plurisubharmonic if and only if it can be written as a composition of a convex function with an analytic function. The decomposition is essentially unique. The result is first established locally, and then Free Universal Monodromy implies the global result. Moreover, we see that plurisubharmonicity is a geometric property-- a real analytic free function plurisubharmonic on a neighborhood is plurisubharmonic on the whole domain. We give an analytic Greene-Liouville theorem, an entire free plurisubharmonic function is a sum of hereditary and antihereditary squares.
