Continued $\mathbf{A_2}$-fractions and singular functions

Continued $\mathbf{A_2}$-fractions and singular functions

In the article we deepen the metric component of theory of infinite $A_2$-continued fractions $[0;a_1,a_2,...,a_n,...]$ with a two-element alphabet $A_2=\{\frac12,1\}$, $a_n\in A_2$ and establish the normal property of numbers of the segment $I=[\frac12;1]$ in terms of their $A_2$-representations: $...

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Bibliographic Details
Main Authors: M.V. Pratsiovytyi, Ya. V. Goncharenko, I.M. Lysenko, S.P. Ratushniak
Format: Article
Language:deu
Published: Ivan Franko National University of Lviv 2022-10-01
Series:Математичні Студії
Subjects:
$a_2$-continued fraction, $a$-representation of numbers, cylinder, basic metric relation, convergent, normal property of number, singular function, cylindrical derivative
Online Access:http://matstud.org.ua/ojs/index.php/matstud/article/view/346
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