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Quasi-equivalence of bases in some Whitney spaces

Part of: Linear function spaces and their duals Approximations and expansions Topological linear spaces and related structures

Published online by Cambridge University Press:  18 May 2021

Alexander Goncharov  and
Yasemin Şengül
Alexander Goncharov*
Affiliation:
Department of Mathematics, Bilkent University, 06800 Ankara, Turkey
Yasemin Şengül
Affiliation:
Faculty of Engineering and Natural Sciences, Sabanci University, Orta Mahalle, Tuzla, 34956 Istanbul, Turkey e-mail: yaseminsengul@sabanciuniv.edu
*
e-mail: goncha@fen.bilkent.edu.tr
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Abstract

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.

Keywords

Topological basesWhitney spacesquasi-equivalence

MSC classification

Primary: 46A35: Summability and bases
Secondary: 46E10: Topological linear spaces of continuous, differentiable or analytic functions 41A10: Approximation by polynomials

Information

Type
Article
Information
Canadian Mathematical Bulletin , Volume 65 , Issue 1 , March 2022 , pp. 106 - 115
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Copyright
© Canadian Mathematical Society 2021

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Footnotes

The research was partially supported by TÜBİTAK (Scientific and Technological Research Council of Turkey), Project 119F023.

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