|
|||||
|
|
Zeros of nonpositive type of generalized Nevanlinna functions with one negative square |
|
| Authors: | Henk de Snoo |
| Affiliation: | a Johann Bernoulli Institute for Mathematics and Computer Science, University of Groningen, P.O. Box 407, 9700 AK Groningen, The Netherlands b Institut für Mathematik, Technische Universität Ilmenau, Curiebau, Weimarer Str. 25, 98693 Ilmenau, Germany c Institute of Mathematics, Jagiellonian University, ?ojasiewicza 6, 30-348 Kraków, Poland |
| 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 defines a path in the closed upper halfplane. Various properties of this path are studied in detail. |
| Keywords: | Pontryagin space Generalized Nevanlinna function Generalized pole of nonpositive type Generalized zero of nonpositive type Integral representation Fractional linear transformation |
| 本文献已被 ScienceDirect 等数据库收录！ | |