A compact set without Markov's property but with an extension operator for $C^∞$-functions

Alexander Goncharov

ArticleOriginal scientific text

Title

A compact set without Markov's property but with an extension operator for $C^{\infty}$ -functions

Authors ^1,²

Affiliations

Department of Mathematics, Bilkent University, 06533 Ankara, Turkey
Department of Mathematics, Civil Building Academy, Rostov-na-Donu, Russia

Abstract

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) \to C^{\infty} [0, 1]

. At the same time, Markov's inequality is not satisfied for certain polynomials on K.

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Title

A compact set without Markov's property but with an extension operator for C∞-functions

Affiliations

Abstract

Bibliography

A compact set without Markov's property but with an extension operator for $C^{\infty}$ -functions