Conditions for the difference set of a central Cantor set to be a Cantorval

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F23%3A00574268" target="_blank" >RIV/67985840:_____/23:00574268 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1007/s00025-023-01940-4" target="_blank" >https://doi.org/10.1007/s00025-023-01940-4</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s00025-023-01940-4" target="_blank" >10.1007/s00025-023-01940-4</a>

Result language
angličtina
Original language name
Conditions for the difference set of a central Cantor set to be a Cantorval
Original language description
Let C(λ) ⊂ [0 , 1] denote the central Cantor set generated by a sequence λ=(λn)∈(0,12)N . By the known trichotomy, the difference set C(λ) - C(λ) of C(λ) is one of three possible sets: a finite union of closed intervals, a Cantor set, or a Cantorval. Our main result describes effective conditions for (λn) which guarantee that C(λ) - C(λ) is a Cantorval. We show that these conditions can be expressed in several equivalent forms. Under additional assumptions, the measure of the Cantorval C(λ) - C(λ) is established. We give an application of the proved theorems for the achievement sets of some fast convergent series.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics

Project
<a href="/en/project/GF20-22230L" target="_blank" >GF20-22230L: Banach spaces of continuous and Lipschitz functions</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2023
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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