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R. Pruckner, H. Woracek:
"Limit behaviour of Nevanlinna functions";
in: "ASC Report 16/2019", issued by: Institute for Analysis and Scientific Computing; Vienna University of Technology, Wien, 2019, ISBN: 978-3-902627-12-4, 1 - 29.

We study the sets of radial or nontangential limit points towards i∞ of a Nevanlinna function q. It is shown that a subset L of C+ is the set of radial limit points of some q, if and only if it is closed, nonempty, and connected. Given L, we explicitly construct a Hamiltonian H such that L is the set of radial and nontangential limit points of the Weyl coefficient qH of the canonical system with Hamiltonian H. Our method is based on a study of the continuous group action of rescaling operators on the set of all Hamiltonians.

Nevanlinna function, limit points, canonical system, Weyl coefficient

http://www.asc.tuwien.ac.at/preprint/2019/asc16x2019.pdf