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- W2952855692 abstract "There are several kinds of universal Taylor series. In one such kind the universal approximation is required at every boundary point of the domain of definition $OO$ of the universal function $f$. In another kind the universal approximation is not required at any point of $partialOO$ but in this case the universal function $f$ can be taken smooth on $oO$ and, moreover, it can be approximated by it's Taylor partial sums on every compact subset of $oO$. Similar generic phenomena hold when the partial sums of the Taylor expansion of the universal function are replaced by some Pad'{e} approximants of it. In the present paper we show that in the case of Pad'{e} approximants, if $OO$ is an open set and $S,T$ are two subsets of $partialOO$ that satisfy some conditions, then there exists a universal function $fin H(OO)$ which is smooth on $OOcup S$ and has some Pad'{e} approximants that approximate $f$ on each compact subset of $OOcup S$ and simultaneously obtain universal approximation on each compact subset of $(CsmoO)cup T$. A sufficient condition for the above to happen is $oScapoT=emptyset$, while a necessary and sufficient condition is not known." @default.
- W2952855692 created "2019-06-27" @default.
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- W2952855692 date "2013-10-05" @default.
- W2952855692 modified "2023-09-27" @default.
- W2952855692 title "Universal Pad'{e} approximants and their behaviour on the boundary" @default.
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