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

• Autorzy: Alexander Goncharov
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 46E10: Topological linear spaces of continuous, differentiable or analytic functions
• 41A17: Inequalities in approximation (Bernstein, Jackson, Nikol\cprime ski{\u\i}-type inequalities)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 1996
• Tom: 119
• Numer: 1
• Strony: 27-35

Daty

wydano

1996

otrzymano

1995-05-10

poprawiono

1996-02-20

Twórcy

autor

Alexander Goncharov

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

Bibliografia

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