Singular functions with applications to fractal dimensions and generalized Takagi functions

DOI10.1007/s10440-011-9665-zzbMath1259.28008OpenAlexW1963886846MaRDI QIDQ1926068

Enrique de Amo, Juan Fernández-Sánchez, Manuel Díaz-Carrillo

Publication date: 27 December 2012

Published in: Acta Applicandae Mathematicae (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10440-011-9665-z

zbMATH Keywords

Schauder basissingular functionHausdorff dimensionTakagi function(simply) normal numbergeneralized dyadic system

Mathematics Subject Classification ID

Fractals (28A80) Hausdorff and packing measures (28A78)

Related Items (12)

Limiting curves for the Pascal adic transformation ⋮ A singular function with a non-zero finite derivative on a dense set ⋮ A study of topological conjugacies between alternate representation systems ⋮ Lineability, spaceability, and latticeability of subsets of \(C([0, 1)\) and Sobolev spaces] ⋮ A new generalization of the Takagi function ⋮ Pisot numbers and strong negations ⋮ Singular distribution functions for random variables with stationary digits ⋮ Unnamed Item ⋮ A general treatment of alternative expectation formulae ⋮ A family of singular functions and its relation to harmonic fractal analysis and fuzzy logic ⋮ Banach spaces and Banach lattices of singular functions ⋮ Random deviations of ergodic sums for the Pascal adic transformation in the case of the Lebesgue measure

Cites Work

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• The Hausdorff dimension of the level sets of Takagi's function
• Measure-preserving functions and the independence copula
• Wavelets on fractals
• Riesz--Nágy singular functions revisited
• Level sets of the Takagi function: Hausdorff dimension
• Wavelets for iterated function systems
• Fibonacci, van der Corput and Riesz-Nágy
• An approach to construct the singular monotone functions by using Markov chains
• A new light on Minkowski's \(?(x)\) function
• Functional equations for peculiar functions
• A total order in \((0,1\) defined through a ``next operator]
• De Rham's singular function and related functions
• Sneaky plasticity and mesoscopic fractals
• On Maxima of Takagi-van der Waerden Functions
• On Van Der Waerden's Nowhere Differentiable Function
• The Takagi function and its generalization
• Ten Lectures on Wavelets
• An Increasing Continuous Singular Function
• Nowhere monotone functions and functions of nonmonotonic type
• On Some Singular Monotonic Functions Which Are Strictly Increasing
• Extreme values of some continuous nowhere differentiable functions

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