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BASES IN SOME SPACES OF WHITNEY FUNCTIONS

2018    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 extension 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.