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      Lebesgue constants on cantor type sets

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      Embargo Lift Date: 2021-03-18
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      Author(s)
      Paksoy, Yaman
      Advisor
      Goncharov, Alexander
      Date
      2020-09
      Publisher
      Bilkent University
      Language
      English
      Type
      Thesis
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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.
      Keywords
      Lebesgue constants
      Cantor type sets
      Faber basis
      Lagrange interpolation
      Permalink
      http://hdl.handle.net/11693/54060
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      • Dept. of Mathematics - Master's degree 128
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