Compositionally universal meromorphic functions

For a sequence of holomorphic maps from a domain to a domain , we consider meromorphic functions f on for which the sequence of compositions is dense in the space of all meromorphic functions on , endowed with the topology of spherically uniform convergence on compact subsets. We generalize and unif...

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Bibliographic Details
Published in:Complex variables and elliptic equations Vol. 64; no. 9; pp. 1534 - 1545
Main Author: Meyrath, Thierry
Format: Journal Article
Language:English
Published: Colchester Taylor & Francis 02.09.2019
Taylor & Francis Ltd
Subjects:
Dmitry Khavinson
Domains
erratic boundary behavior
Mathematical analysis
Meromorphic functions
spherical approximation
Topology
Universality
ISSN:1747-6933, 1747-6941
Online Access:Get full text
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Summary:For a sequence of holomorphic maps from a domain to a domain , we consider meromorphic functions f on for which the sequence of compositions is dense in the space of all meromorphic functions on , endowed with the topology of spherically uniform convergence on compact subsets. We generalize and unify several known results about universal meromorphic functions and provide new examples of sequences of holomorphic maps, for which there exist universal meromorphic functions. We also consider meromorphic functions that have in some sense a maximally erratic boundary behavior in general domains , . As a corollary, we obtain that meromorphic functions on general domains are generically non-extendable.
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ISSN:1747-6933
1747-6941
DOI:10.1080/17476933.2018.1538213