论文标题
在几个变量中使用阳性半明确函数和Nevanlinna内核的Herglotz-Nevanlinna函数的表征
Characterizations of Herglotz-Nevanlinna functions using positive semi-definite functions and the Nevanlinna kernel in several variables
论文作者
论文摘要
在本文中，我们通过特定类型的阳性半明确函数（称为泊松型函数）给出了Herglotz-Nevanlinna函数的几个特征。这使我们能够提出经典Nevanlinna内核的多维类似物，并在几个变量中对广义nevanlinna函数的定义进行定义。此外，还给出了Herglotz-Nevanlinna函数的对称扩展的特征。还讨论了Loewner函数的子类，以及对具有非负实际部分的单位polydisk上的全态函数的解释。
In this paper, we give several characterizations of Herglotz-Nevanlinna functions in terms of a specific type of positive semi-definite functions called Poisson-type functions. This allows us to propose a multidimensional analogue of the classical Nevanlinna kernel and a definition of generalized Nevanlinna functions in several variables. Furthermore, a characterization of the symmetric extension of a Herglotz-Nevanlinna function is also given. The subclass of Loewner functions is also discussed, as well as an interpretation of the main result in terms of holomorphic functions on the unit polydisk with non-negative real part.
