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- W4289294801 abstract "Let $E$ be a closed subset of the unit circle of measure zero. Recently, Beise and Muller showed the existence of a function in the Hardy space $H^2$ for which the partial sums of its Taylor series approximate any continuous function on $E$. In this paper, we establish an analogue of this result in a non-linear setting where we consider optimal polynomial approximants of reciprocals of functions in $H^2$ instead of Taylor polynomials. The proof uses a new result on simultaneous zero-free approximation of independent interest. Our results extend to Dirichlet-type spaces $mathcal{D}_alpha$ for $alpha in [0,1]$." @default.
- W4289294801 created "2022-08-02" @default.
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- W4289294801 date "2018-11-10" @default.
- W4289294801 modified "2023-09-26" @default.
- W4289294801 title "Simultaneous zero-free approximation and universal optimal polynomial approximants" @default.
- W4289294801 doi "https://doi.org/10.48550/arxiv.1811.04308" @default.
- W4289294801 hasPublicationYear "2018" @default.
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