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Please use this identifier to cite or link to this item: http://enpuir.npu.edu.ua/handle/123456789/10661
Title: On one class of functions related to Ostrogradsky series and containing singular and nowhere monotonic functions
Authors: Albeverio, Sergio
Baranovskyi, Oleksandr
Kondratiev, Yuri
Pratsiovytyi, Mykola
Keywords: first Ostrogradsky series
representation of real number
infinite system of functional equations
singular function
nowhere monotonic function
Lebesgue measure
fractal Hausdorff–Besicovitch dimension
Issue Date: 2013
Publisher: Вид-во НПУ ім. М. П. Драгоманова
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.
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.
URI: http://enpuir.npu.edu.ua/handle/123456789/10661
Appears in Collections:Випуск 15

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