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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Ulam-Zahorski problem on free interpolation by smooth functions


Author: A. Olevskiĭ
Journal: Trans. Amer. Math. Soc. 342 (1994), 713-727
MSC: Primary 26A48; Secondary 26A51, 41A05
MathSciNet review: 1179399
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Abstract: Let f be a function belonging to $ {C^n}[0,1]$. Is it possible to find a smoother function $ g \in {C^{n + 1}}$ (or at least $ {C^{n + \varepsilon }}$) which has infinitely many points of contact of maximal order n with f (or at least arbitrarily many such points with fixed norm $ {\left\Vert g \right\Vert _{{C^{n + \varepsilon }}}}$)? It turns out that for n = 0 and 1 the answer is positive, but if $ n \geq 2$, it is negative. This gives a complete solution to the Ulam-Zahorski question on free interpolation on perfect sets.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1994-1179399-9
PII: S 0002-9947(1994)1179399-9
Article copyright: © Copyright 1994 American Mathematical Society