Browsing by Subject "Extension problem"

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    Bases in some spaces of Whitney functions
    (Duke University Press, 2017-06) Goncharov, Alexander; Ural, Zeliha
    We construct topological bases in spaces of Whitney functions on Cantor sets, which were introduced by the first author. By means of suitable individual extensions of basis elements, we construct a linear continuous exten- sion operator, when it exists for the corresponding space. In general, elements of the basis are restrictions of polynomials to certain subsets. In the case of small sets, we can present strict polynomial bases as well.
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    Mityagin’s extension problem. Progress report
    (Elsevier, 2017-04-01) Goncharov, A.; Ural, Z.
    Given a compact set K⊂Rd, let E(K)denote the space of Whitney jets onK. The compact set Kis said to have the extension property if there exists a continuous linear extension operator W:E(K) −→C∞(Rd). 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.