Lebesgue constants on cantor type sets
Author(s)
Advisor
Goncharov, AlexanderDate
2020-09Publisher
Bilkent University
Language
English
Type
ThesisItem Usage Stats
292
views
views
117
downloads
downloads
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.