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

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Ukrainian Mathematical Journal Aims and scope

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.).

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Authors and Affiliations

  1. Institute of Mathematics, Ukrainian National Academy of Sciences, Kyiv, Ukraine

    M. V. Prats’ovytyi & A.V. Kalashnikov

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  1. M. V. Prats’ovytyi
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  2. A.V. Kalashnikov
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 65, No. 3, pp. 405–417, March, 2013.

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Prats’ovytyi, M.V., Kalashnikov, A. Self-Affine Singular and Nowhere Monotone Functions Related to the Q-Representation of Real Numbers. Ukr Math J 65, 448–462 (2013). https://doi.org/10.1007/s11253-013-0788-4

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  • DOI: https://doi.org/10.1007/s11253-013-0788-4

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