Reference : Compositionally universal meromorphic functions
Scientific journals : Article
Physical, chemical, mathematical & earth Sciences : Mathematics
Compositionally universal meromorphic functions
Meyrath, Thierry mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit]
Complex Variables and Elliptic Equations
Taylor & Francis
Yes (verified by ORBilu)
United Kingdom
[en] Universality ; Spherical approximation ; Meromorphic functions ; Erratic boundary behavior
[en] For a sequence of holomorphic maps $(\vp_n)$ from a domain $\Omega_2$ to a domain $\Omega_1$, we consider meromorphic functions $f$ on $\Omega_1$ for which the sequence of compositions $(f \circ \vp_n)$ is dense in the space of all meromorphic functions on $\Omega_2$, 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 $\Omega \subset \C, \Omega \neq \C$. As a corollary, we obtain that meromorphic functions on general domains are generically non-extendable.

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