Limit behavior of Weyl coefficients

Pruckner, R.; Woracek, H.

doi:10.1090/spmj/1729

Limit behavior of Weyl coefficients
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by R. Pruckner and H. Woracek

St. Petersburg Math. J. 33 (2022), 849-865

DOI: https://doi.org/10.1090/spmj/1729

Published electronically: August 24, 2022

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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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