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February 2018 Bases in some spaces of Whitney functions
Alexander Goncharov, Zeliha Ural
Ann. Funct. Anal. 9(1): 56-71 (February 2018). DOI: 10.1215/20088752-2017-0024

Abstract

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.

Citation

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Alexander Goncharov. Zeliha Ural. "Bases in some spaces of Whitney functions." Ann. Funct. Anal. 9 (1) 56 - 71, February 2018. https://doi.org/10.1215/20088752-2017-0024

Information

Received: 23 August 2016; Accepted: 7 February 2017; Published: February 2018
First available in Project Euclid: 29 June 2017

zbMATH: 06841341
MathSciNet: MR3758743
Digital Object Identifier: 10.1215/20088752-2017-0024

Subjects:
Primary: 46E10
Secondary: 28A80 , 46A35

Keywords: extension problem , topological bases , Whitney spaces

Rights: Copyright © 2018 Tusi Mathematical Research Group

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Vol.9 • No. 1 • February 2018
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