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1996 | 119 | 1 | 27-35
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A compact set without Markov's property but with an extension operator for $C^∞$-functions

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We give an example of a compact set K ⊂ [0, 1] such that the space ℇ(K) of Whitney functions is isomorphic to the space s of rapidly decreasing sequences, and hence there exists a linear continuous extension operator $L: ℇ(K) → C^{∞}[0,1]$. At the same time, Markov's inequality is not satisfied for certain polynomials on K.
Słowa kluczowe
  • Department of Mathematics, Bilkent University, 06533 Ankara, Turkey,
  • Department of Mathematics, Civil Building Academy, Rostov-na-Donu, Russia
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