Abstract:The sets of radial or nontangential limit points towards $i\infty$ of a Nevanlinna function $q$ are studied. Given a nonempty, closed, and connected subset ${\mathcal {L}}$ of $\overline {{\mathbb {C}}_+}$, a Hamiltonian $H$ is constructed explicitly such that the radial and outer angular cluster sets towards $i\infty$ of the Weyl coefficient $q_H$ are both equal to ${\mathcal {L}}$. The method is based on a study of the continuous group action of rescaling operators on the set of all Hamiltonians.

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中文翻译：

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外尔系数的极限行为

摘要：研究了 Nevanlinna 函数 $q$ 的径向或非切向极限点集合。给定一个 $\overline {{\mathbb {C}}_+}$ 的非空、闭合和连通子集 ${\mathcal {L}}$，一个哈密顿量 $H$ 被显式构造，使得径向和外角朝向 Weyl 系数 $q_H$ 的 $i\infty$ 的簇集都等于 ${\mathcal {L}}$。该方法基于对所有哈密顿量集合上的重新缩放算子的连续群作用的研究。

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