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arXiv · 1306.1117

Global and local behavior of zeros of nonpositive type

Henk de Snoo·Henrik Winkler·Michal Wojtylak
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Abstract

A generalized Nevanlinna function $Q(z)$ with one negative square has precisely one generalized zero of nonpositive type in the closed extended upper halfplane. The fractional linear transformation defined by $Q_\tau(z)=(Q(z)-\tau)/(1+\tau Q(z))$, $\tau \in \mathbf{Real} \cup \{\infty\}$, is a generalized Nevanlinna function with one negative square. Its generalized zero of nonpositive type $\alpha(\tau)$ as a function of $\tau$ is being studied. In particular, it is shown that it is continuous and its behavior in the points where the function extends through the real line is investigated.

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Henk de Snoo, Henrik Winkler, Michal Wojtylak. 2013-05-31. Global and local behavior of zeros of nonpositive type. https://arxiv.org/abs/1306.1117

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