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Compositionally universal meromorphic functions Meyrath, Thierry in Complex Variables and Elliptic Equations (2019), 64(9), 1534-1545 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 ... [more ▼] 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. [less ▲] Detailed reference viewed: 137 (11 UL)On two classes of universal meromorphic functions Meyrath, Thierry in Complex Variables and Elliptic Equations (2013), 58(10), 1343-1354 We consider two classes of meromorphic functions, which have universal approximation properties with respect to translations, and prove that both are residual subsets of the space of all meromorphic ... [more ▼] We consider two classes of meromorphic functions, which have universal approximation properties with respect to translations, and prove that both are residual subsets of the space of all meromorphic functions. Furthermore, we show that the two classes do not coincide. [less ▲] Detailed reference viewed: 146 (7 UL)An extension result of CR functions by a general Schwarz re ection principle Hui, Chun Yin in Complex Variables and Elliptic Equations (2009), 54 Detailed reference viewed: 37 (1 UL) |
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