Lebesgue constants on cantor type sets

Date
2020-09
Advisor
Goncharov, Alexander
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Bilkent University
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English
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Abstract

The properties of compact subsets of the real line which are in the class of Bounded Lebesgue Constants (BLC) are investigated. Knowing that any such set must have 1-dimensional Lebesgue measure zero and nowhere density, and the fact that there are examples of countable sets both inside and outside of the class BLC, families of Cantor-type sets were focused on. Backed up by numerical experiments (up to degree 128) and analytical results, the conjecture “there exists no perfect set in BLC” was put forward.

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Keywords
Lebesgue constants, Cantor type sets, Faber basis, Lagrange interpolation
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Published Version (Please cite this version)