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A note on dyadic approximation in Cantor's set
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Allen, Demi, Baker, Simon, Chow, Sam and Yu, Han (2022) A note on dyadic approximation in Cantor's set. Indagationes Mathematicae . doi:10.1016/j.indag.2022.11.002 ISSN 0019-3577. [ (🔓): Yes ]. (In Press)
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Official URL: https://doi.org/10.1016/j.indag.2022.11.002
Abstract
We consider the convergence theory for dyadic approximation in the middle-third Cantor set, , for approximation functions of the form (). In particular, we show that for values of beyond a certain threshold we have that almost no point in is dyadically -well approximable with respect to the natural probability measure on . This refines a previous result in this direction obtained by the first, third, and fourth named authors.
| Item Type: | Journal Article | |||||||||
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| Subjects: | Q Science > QA Mathematics | |||||||||
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | |||||||||
| Library of Congress Subject Headings (LCSH): | Diophantine approximation , Cantor sets , Fourier analysis | |||||||||
| Journal or Publication Title: | Indagationes Mathematicae | |||||||||
| Publisher: | Elsevier | |||||||||
| ISSN: | 0019-3577 | |||||||||
| Official Date: | 2022 | |||||||||
| Dates: |
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| DOI: | 10.1016/j.indag.2022.11.002 | |||||||||
| Status: | Peer Reviewed | |||||||||
| Publication Status: | In Press | |||||||||
| Access rights to Published version: | Open Access (Creative Commons) | |||||||||
| Date of first compliant deposit: | 7 November 2022 | |||||||||
| RIOXX Funder/Project Grant: |
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