Simple proofs of nowhere-differentiability for Weierstrass's function and cases of slow growth

DOI10.1007/s00041-009-9072-2zbMath1194.26005arXiv1610.06354OpenAlexW3104785124MaRDI QIDQ2380387

Johnsen, Jon.

Publication date: 26 March 2010

Published in: The Journal of Fourier Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1610.06354

zbMATH Keywords

Weierstrass functionlacunary Fourier seriessecond microlocalisationNowhere differentiability

Mathematics Subject Classification ID

Nondifferentiability (nondifferentiable functions, points of nondifferentiability), discontinuous derivatives (26A27)

Related Items (4)

Fractal functions with continuous Weil-type derivatives of variable order in control of distributed systems ⋮ Fundamental results for pseudo-differential operators of type \(1, 1\) ⋮ About the uniform Hölder continuity of generalized Riemann function ⋮ Sharp estimates for the covering numbers of the Weierstrass fractal kernel

Cites Work

• The differentiability of Fourier gap series and ``Riemann's example of a continuous, nondifferentiable function
• Old friends revisited: The multifractal nature of some classical functions
• Über trigonometrische Approximation und Fouriersche Reihen
• The nondifferentiability of Weierstrass' function
• Some Fourier series with gaps
• Type 1,1-Operators Defined by Vanishing Frequency Modulation
• A Nowhere Differentiable Continuous Function Constructed by Infinite Products
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