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arXiv · 1011.2081

Zeros of nonpositive type of generalized Nevanlinna functions with one negative square

H. S. V. de Snoo·H. Winkler·M. 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 $Q_τ(z)=(Q(z)-τ)/(1+τQ(z))$, $τ\in \mathbb{R} \cup \{\infty\}$, is a generalized Nevanlinna function with one negative square. Its generalized zero of nonpositive type $α(τ)$ as a function of $τ$ defines a path in the closed upper halfplane. Various properties of this path are studied in detail.

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H. S. V. de Snoo, H. Winkler, M. Wojtylak. 2010-11-09. Zeros of nonpositive type of generalized Nevanlinna functions with one negative square. https://arxiv.org/abs/1011.2081

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