Publication: On one class of functions related to Ostrogradsky series and containing singular and nowhere monotonic functions
Loading...
Date
Authors
Albeverio, Sergio
Baranovskyi, Oleksandr
Kondratiev, Yuri
Pratsiovytyi, Mykola
Journal Title
Journal ISSN
Volume Title
Publisher
Вид-во НПУ ім. М. П. Драгоманова
Abstract
We study structural, diferential, fractal properties of function F according to the sequence (pn). “Most” of such functions are singular and nowhere monotonic, and singular non-monotonic functions form an essential class of them. We prove that function is nowhere monotonic if the sequence (pn) does not have zeroes but has negative terms.
Description
Keywords
first Ostrogradsky series, representation of real number, infinite system of functional equations, singular function, nowhere monotonic function, Lebesgue measure, fractal Hausdorff–Besicovitch dimension
Citation
Albeverio, S. On one class of functions related to Ostrogradsky series and containing singular and nowhere monotonic functions / Albeverio Sergio, Baranovskyi Oleksandr, Kondratiev Yuri, Pratsiovytyi Mykola // Науковий часопис Національного педагогічного університету iменi М. П. Драгоманова. Серiя 1. Фiзико-математичнi науки : зб. наук. праць. – Київ : Вид-во НПУ iменi М. П. Драгоманова, 2013. – Вип. 15. – С. 35-55.