Subclasses of Universal Taylor Series and center independence

Vagia Vlachou

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arXiv · 2002.03304

Subclasses of Universal Taylor Series and center independence

Vagia Vlachou

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Abstract

A holomorphic function f on a simply connected domain $\Omega$ belongs to a subclass of universal Taylor series if prescribed and infinite number of partial sums of the Taylor expansion of f around a given center $\zeta_0$ realize Mergalyan-type approximations outside $\Omega$. We will prove that this class is independent of the choice of center if the indices of the partial sums do not grow very fast to infinity.

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Vagia Vlachou. 2020-02-09. Subclasses of Universal Taylor Series and center independence. https://arxiv.org/abs/2002.03304

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