Non-differentiability and Hölder properties of self-affine functions

DOI10.1016/j.exmath.2017.10.002zbMath1391.65039OpenAlexW2767506723MaRDI QIDQ1639658

Serge Dubuc

Publication date: 13 June 2018

Published in: Expositiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.exmath.2017.10.002

zbMATH Keywords

non-differentiabilityHölder conditionself-affine function

Mathematics Subject Classification ID

Lipschitz (Hölder) classes (26A16) Computer-aided design (modeling of curves and surfaces) (65D17) Nondifferentiability (nondifferentiable functions, points of nondifferentiability), discontinuous derivatives (26A27)

Related Items (4)

The pointwise Hölder spectrum of general self-affine functions on an interval ⋮ Continuous Maps Admitting No Tangent Lines: A Centennial of Besicovitch Functions ⋮ Absolute continuity in higher dimensions ⋮ The subdivision schemes of Besicovitch and Cantor

Cites Work

• The Takagi function: a survey
• On continuous functions with no unilateral derivatives
• Hölder exponents and box dimension for self-affine fractal functions
• Functions with prescribed Hölder exponent
• Self-affine fractal functions and wavelet series
• The Cantor function
• Continuous Nowhere-Differentiable Functions--an Application of Contraction Mappings
• Probabilistic Behaviour of Functions in the Zygmund Spaces ∧ ^* and λ ^*
• The Takagi Function and Its Properties
• On Asymmetrical Derivates of Non-Differentiable Functions
• On Some Singular Monotonic Functions Which Are Strictly Increasing
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