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

2010/11/09 by H. S. V. de Snoo, de Snoo, H. S. V., Henrik Winkler +5 · 1 citation
Mathematics · #Differential Equations and Numerical Methods #Numerical methods for differential equations #Spectral Theory in Mathematical Physics #math.FA #msc:47A05 #msc:47A06

paper · pdf · doi:10.48550/arxiv.1011.2081

arxiv created 2010/11/09 · arxiv updated 2010/11/10

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∈ ℝ ∪ \∞\, 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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