论文标题
关于Nevanlinna测量的结构
On the structure of Nevanlinna measures
论文作者
论文摘要
在本文中，我们研究了Nevanlinna度量的结构特性，即Herglotz-Nevanlinna函数的整体表示中出现的Borel度量。特别是，我们根据它们的傅立叶变换给出了这些度量的表征，它表征了包括极端措施在内的超级措施的措施，描述了措施的奇异部分的结构时，当某些变量设置为固定值时，并提供了扩展和收缩立方体的衡量标准。在适用的情况下，在polydisc的环境中也表示相应的结果，我们的某些证据实际上是通过polydisc完善的。
In this paper, we study the structural properties of Nevanlinna measures, i.e. Borel measures that arise in the integral representation of Herglotz-Nevanlinna functions. In particular, we give a characterization of these measures in terms of their Fourier transform, characterize measures supported on hyperplanes including extremal measures, describe the structure of the singular part of the measures when some variable are set to a fixed value, and provide estimates for the measure of expanding and shrinking cubes. Corresponding results are stated also in the setting of the polydisc where applicable, and some of our proofs are actually perfomed via the polydisc.
