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- W1645300387 abstract "We prove the existence of holomorphic functions $f$ defined on any open convex subset ${rm Omega}subset {{mathbb C}}^n$, whose partial sums of the Taylor developments approximate uniformly any complex polynomial on any convex compact set disjoint from $bar{{rm Omega}}$ and on denumerably many convex compact sets in ${{mathbb C}}^nbackslash {rm Omega}$ which may meet the boundary $partial {rm Omega}$. If the universal approximation is only required on convex compact sets disjoint from $bar{{rm Omega}}$, then $f$ may be chosen to be smooth on $partial {rm Omega}$, that is $fin A^{infty}({rm Omega})$. Those are generic universalities." @default.
- W1645300387 created "2016-06-24" @default.
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- W1645300387 date "2013-02-17" @default.
- W1645300387 modified "2023-09-27" @default.
- W1645300387 title "Universal Taylor Series On Convex Subsets Of $Mathbb{C}^{N}$" @default.
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