Article (Scientific journals)
Universal meromorphic approximation on Vitushkin sets
Luh, Wolfgang; Meyrath, Thierry; Niess, Markus
2008In Journal of Contemporary Mathematical Analysis, 43 (6), p. 365-371
Peer reviewed
 

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Keywords :
Universality; rational and meromorphic approximation; Vitushkin sets
Abstract :
[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].
Disciplines :
Mathematics
Author, co-author :
Luh, Wolfgang;  Universität Trier > Fachbereich IV - Mathematik
Meyrath, Thierry ;  Universität Trier > Fachbereich IV - Mathematik
Niess, Markus;  Katholische Universität Eichstätt-Ingolstadt
Language :
English
Title :
Universal meromorphic approximation on Vitushkin sets
Publication date :
2008
Journal title :
Journal of Contemporary Mathematical Analysis
ISSN :
1068-3623
Volume :
43
Issue :
6
Pages :
365-371
Peer reviewed :
Peer reviewed
Available on ORBilu :
since 20 May 2013

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