RUS  ENG
Полная версия
ЖУРНАЛЫ // Журнал математической физики, анализа, геометрии // Архив

Журн. матем. физ., анал., геом., 2018, том 14, номер 2, страницы 197–213 (Mi jmag697)

Эта публикация цитируется в 14 статьях

Non-differentiable functions defined in terms of classical representations of real numbers

S. O. Serbenyuk

Institute of Mathematics of the National Academy of Sciences of Ukraine, 3 Tereschenkivska St., Kyiv, 01004, Ukraine

Аннотация: The present paper is devoted to the functions from a certain subclass of non-differentiable functions. The arguments and values of the considered functions are represented by the $s$-adic representation or the nega-$s$-adic representation of real numbers. The technique of modeling these functions is the simplest as compared with the well-known techniques of modeling non-differentiable functions. In other words, the values of these functions are obtained from the $s$-adic or nega-$s$-adic representation of the argument by a certain change of digits or combinations of digits. Integral, fractal and other properties of the functions are described.

Ключевые слова и фразы: nowhere differentiable function, $s$-adic representation, nega-$s$-adic representation, non-monotonic function, Hausdorff–Besicovitch dimension.

MSC: 26A27, 11B34, 11K55, 39B22

Поступила в редакцию: 09.05.2017
Исправленный вариант: 17.07.2017

Язык публикации: английский

DOI: 10.15407/mag14.02.197



© МИАН, 2024