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1 results

Quasi-equivalence of bases in some Whitney spaces
Part of
Alexander Goncharov, Yasemin Şengül
Journal:

Canadian Mathematical Bulletin / Volume 65 / Issue 1 / March 2022

Published online by Cambridge University Press:

18 May 2021, pp. 106-115

Print publication:

March 2022
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If the logarithmic dimension of a Cantor-type set K is smaller than $1$ , then the Whitney space $\mathcal {E}(K)$ possesses an interpolating Faber basis. For any generalized Cantor-type set K, a basis in $\mathcal {E}(K)$ can be presented by means of functions that are polynomials locally. This gives a plenty of bases in each space $\mathcal {E}(K)$ . We show that these bases are quasi-equivalent.