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

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

2010-11-09

arxiv.org/abs/1011.2081v1

Mathematics

Functional Analysis

Scientific paper

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 $Q_\tau(z)=(Q(z)-\tau)/(1+\tau Q(z))$, $\tau \in \mathbb{R} \cup \{\infty\}$, is a generalized Nevanlinna function with one negative square. Its generalized zero of nonpositive type $\alpha(\tau)$ as a function of $\tau$ defines a path in the closed upper halfplane. Various properties of this path are studied in detail.

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