[en] Universality ; rational and meromorphic approximation ; Vitushkin sets
[en] 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].
[Universität Trier > Fachbereich IV - Mathematik]
