Self-Affine Singular and Nowhere Monotone Functions Related to the Q-Representation of Real Numbers

We study functional, differential, integral, self-affine, and fractal properties of continuous functions from a finite-parameter family of functions with a continual set of “peculiarities.” Almost all functions in this family are singular (their derivative is equal to zero almost everywhere in a sen...

Full description

Saved in:
Bibliographic Details
Published in:Ukrainian mathematical journal 2013-08, Vol.65 (3), p.448-462
Main Authors: Prats’ovytyi, M. V., Kalashnikov, A.V.
Format: Article
Language:English
Subjects:
Algebra
Analysis
Applications of Mathematics
Geometry
Mathematics
Mathematics and Statistics
Statistics
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We study functional, differential, integral, self-affine, and fractal properties of continuous functions from a finite-parameter family of functions with a continual set of “peculiarities.” Almost all functions in this family are singular (their derivative is equal to zero almost everywhere in a sense of the Lebesgue measure) or nowhere monotone and, in particular, not differentiable. We consider various approaches to the definition of these functions (by using a system of functional equations, projectors of the symbols of various representations, distributions of random variables, etc.).
ISSN:0041-5995
1573-9376
DOI:10.1007/s11253-013-0788-4