Ulam-zahorski problem on free interpolation by smooth functions

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Let f be a function belonging to Cn[0, 1]. Is it possible to find a smoother function g ϵ Cn+1(or at least Cn+ε) which has infinitely many points of contact of maximal order n with f (or at least arbitrarily many such points with fixed norm g Cn+ε)? It turns out that for n = 0 and 1 the answer is positive, but if n ≥ 2, it is negative. This gives a complete solution to the Ulam-Zahorski question on free interpolation on perfect sets.

Original languageEnglish
Pages (from-to)713-727
Number of pages15
JournalTransactions of the American Mathematical Society
Issue number2
StatePublished - Apr 1994


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