使用半正定函数与多变量Nevanlinna核的Herglotz-Nevanlinna函数的刻画
Characterizations of Herglotz-Nevanlinna functions using positive semi-definite functions and the Nevanlinna kernel in several variables
AI总结：
本文利用Poisson型半正定函数刻画了Herglotz-Nevanlinna函数，提出了多维Nevanlinna核与多变量广义Nevanlinna函数的定义，并探讨了其对称扩张、Loewner函数子类及单位多圆盘上的全纯函数解释。
摘要：
本文利用称为Poisson型函数的特定半正定函数，给出了Herglotz-Nevanlinna函数的若干刻画。这使我们能够提出经典Nevanlinna核的多维类似物，以及多变量广义Nevanlinna函数的定义。此外，还给出了Herglotz-Nevanlinna函数对称扩张的刻画。同时讨论了Loewner函数子类，以及主要结果在实部非负的单位多圆盘全纯函数方面的解释。
英文摘要：
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.
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。
