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See detailUniversal meromorphic approximation on Vitushkin sets
Luh, Wolfgang; Meyrath, Thierry UL; Niess, Markus

in Journal of Contemporary Mathematical Analysis (2008), 43(6), 365-371

The paper proves the following result on universal meromorphic approximation: Given any unbounded sequence {λ_n} ⊂ \C, there exists a function φ, meromorphic on \C, with the following property. For every ... [more ▼]

The paper proves the following result on universal meromorphic approximation: Given any unbounded sequence {λ_n} ⊂ \C, there exists a function φ, meromorphic on \C, with the following property. For every compact set K of rational approximation (i.e. Vitushkin set), and every function f, continuous on K and holomorphic in the interior of K, there exists a subsequence {n_k} of \N such that {φ(z + λ_{n_k})} converges to f(z) uniformly on K. A similar result is obtained for arbitrary domains G \neq \C. Moreover, in case {λ_n} = {n} the function φ is frequently universal in terms of Bayart/Grivaux [3]. [less ▲]

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