Universal partial sums of Taylor series as functions of the centre of\n expansion

2017/10/09 by Christoforos Panagiotis, Panagiotis, Christoforos
Mathematics · #Holomorphic and Operator Theory #Meromorphic and Entire Functions #Advanced Banach Space Theory

paper · pdf · doi:10.48550/arxiv.1710.03114

Abstract

V. Nestoridis conjectured that if \Ω is a simply connected subset of\n\ℂ that does not contain 0 and S(\Ω) is the set of all\nfunctions f\∈ \H(\Ω) with the property that the set\n \T_N(f)(z) coloneqq\∑_n=0^N dfracf⁽ⁿ⁾(z)n! (-z)ⁿ : N =\n0,1,2,\… \ is dense in \H(\Ω), then S(\Ω) is a\ndense G_\δ set in \H(\Ω). We answer the conjecture in the\naffirmative in the special case where \Ω is an open disc D(z₀,r) that\ndoes not contain 0.\n

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