Global and local behavior of zeros of nonpositive type

2013/05/31 by Henk de Snoo, de Snoo, Henk, Henrik Winkler +3
Mathematics · #47A06 #Complex Variables (math.CV) #FOS: Mathematics #Functional Analysis (math.FA) #Primary 47A05 #math.CV #math.FA #msc:47A05 #msc:47A06

paper · pdf · doi:10.48550/arxiv.1306.1117

arxiv created 2013/05/31 · arxiv updated 2013/06/06

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∈ Real ∪ \∞\, is a generalized Nevanlinna function with one negative square. Its generalized zero of nonpositive type α(τ) as a function of τ 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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