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Universal distribution of limit points Meyrath, Thierry ; in Acta Mathematica Hungarica (2011), 133(3), 288-303 We consider sequences of functions that have in some sense a universal distribution of limit points of zeros in the complex plane. In particular, we prove that functions having universal approximation ... [more ▼] We consider sequences of functions that have in some sense a universal distribution of limit points of zeros in the complex plane. In particular, we prove that functions having universal approximation properties on compact sets with connected complement automatically have such a universal distribution of limit points. Moreover, in the case of sequences of derivatives, we show connections between this kind of universality and some rather old results of Edrei/MacLane and Pólya. Finally, we show the lineability of the set of what we call Jentzsch-universal power series. [less ▲] Detailed reference viewed: 47 (1 UL)Universal meromorphic approximation on Vitushkin sets ; Meyrath, Thierry ; 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 ▲] Detailed reference viewed: 47 (3 UL) |
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