论奈万林纳量纲的结构

Pub Date : 2024-03-03 DOI:10.1002/mana.202200135
Mitja Nedic, Eero Saksman
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引用次数: 0

摘要

本文研究 Nevanlinna 度量的结构特性,即在 Herglotz-Nevanlinna 函数积分表示中出现的 Borel 度量。特别是,我们给出了这些量的傅立叶变换特征,描述了支持在超平面上的量的特征,包括极值量,描述了当一些变量被设为固定值时量的奇异部分的结构,并给出了膨胀和收缩立方体的量的估计值。在适用的情况下,相应的结果也会在多圆盘的环境中陈述,我们的一些证明实际上是通过多圆盘进行的。
本文章由计算机程序翻译,如有差异,请以英文原文为准。

On the structure of Nevanlinna measures

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On the structure of Nevanlinna measures

In this paper, we study the structural properties of Nevanlinna measures, that is, 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 performed via the polydisc.

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