Limit behaviour of Weyl coefficients

We study the sets of radial or nontangential limit points towards i∞ of a Nevanlinna function q. Given a nonempty, closed, and connected subset L of C+, we explicitly construct a Hamiltonian H such that the radialand outer angular cluster sets towards i∞ of the Weyl coefficient qH are both equal to L. Our method is based on a study of the continuous group action of rescaling operators on the set of all Hamiltonians. AMS MSC 2010: 34B20, 30D40, 37J99, 30J99

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