Universality vs. non-normality of families of meromorphic functions
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- by L. Bernal-González, A. Jung and J. Müller PDF
- Proc. Amer. Math. Soc. 149 (2021), 761-771 Request permission
Abstract:
For a family $\mathcal {F}=\{f_n:n\in \mathbb {N}\}$ of meromorphic functions on an open set $\Omega \subset \mathbb {C}$, we will establish several connections between the property that $\mathcal {F}$ is a universal family, i.e., that restrictions of $\mathcal {F}$ to suitable subsets of $\Omega$ are dense families in the corresponding function spaces, and the property that $\mathcal {F}$ is a non-normal family.References
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Additional Information
- L. Bernal-González
- Affiliation: Departamento de Análisis Matemático, Facultad de Matemáticas, Instituto de Matemáticas, Antonio de Castro Brzezicki, Universidad de Sevilla, Avenida Reina Mercedes, 41080 Sevilla, Spain
- Email: lbernal@us.es
- A. Jung
- Affiliation: Fachbereich IV Mathematik, Universität Trier, D-54286 Trier, Germany
- MR Author ID: 1183438
- Email: andreas.tibor.jung@gmail.com
- J. Müller
- Affiliation: Fachbereich IV Mathematik, Universität Trier, D-54286 Trier, Germany
- ORCID: 0000-0002-5872-0129
- Email: jmueller@uni-trier.de
- Received by editor(s): September 3, 2019
- Received by editor(s) in revised form: June 16, 2020
- Published electronically: December 16, 2020
- Additional Notes: The first author was supported by the Plan Andaluz de Investigación de la Junta de Andalucía FQM-127 Grant P08-FQM-03543 and by MICINN Grant PGC2018-098474-B-C21.
The second author was supported by DFG-Forschungsstipendium JU 3067/1-1. - Communicated by: Filippo Bracci
- © Copyright 2020 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 149 (2021), 761-771
- MSC (2010): Primary 30K99, 30D45, 37F10
- DOI: https://doi.org/10.1090/proc/15237
- MathSciNet review: 4198081