Mityagin's Extension Problem. Progress Report

2016/06/28 by Alexander Goncharov, Goncharov, Alexander, Zeliha Ural +1
Mathematics · #31A15 #41A10 #46E10 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Analysis (math.FA) #math.CA #math.FA #msc:31A15 #msc:41A10 #msc:46E10

paper · pdf · doi:10.48550/arxiv.1606.08606

arxiv created 2016/06/28 · arxiv updated 2016/06/29

Abstract

Given a compact set K⊂ \Bbb R^d, let \mathcal E(K) denote the space of Whitney jets on K. The compact set K is said to have the extension property if there exists a continuous linear extension operator W:\mathcal E(K) \longrightarrow C^∞(\Bbb R^d). In 1961 B. S. Mityagin posed a problem to give a characterization of the extension property in geometric terms. We show that there is no such complete description in terms of densities of Hausdorff contents or related characteristics. Also the extension property cannot be characterized in terms of growth of Markov's factors for the set.

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