Global and local behavior of zeros of nonpositive type |
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Authors: | Henk de Snoo Henrik Winkler Michał Wojtylak |
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Affiliation: | 1. Johann Bernoulli Institute for Mathematics and Computer Science, University of Groningen, P.O. Box 407, 9700 AK Groningen, Netherlands;2. Institut für Mathematik, Technische Universität Ilmenau, Curiebau, Weimarer Str. 25, 98693 Ilmenau, Germany;3. Institute of Mathematics, Jagiellonian University, ul. ?ojasiewicza 6, 30-348 Kraków, Poland |
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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 Qτ(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 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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Keywords: | Generalized Nevanlinna function Generalized zero of nonpositive type Generalized pole of nonpositive type |
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