Differentiability and dimension of some fractal Fourier series

DOI10.1006/aima.1998.1792zbMath0930.42002OpenAlexW1985206526MaRDI QIDQ1283431

Fernando Chamizo, Antonio Córdoba

Publication date: 13 April 1999

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://semanticscholar.org/paper/f0ce0f05eb1aa0390ab65f9ce558d7f485b32777

zbMATH Keywords

Fourier seriesfractal dimensionWeyl sumsWeyl inequalitiesRiemann's function

Mathematics Subject Classification ID

Fractals (28A80) Fourier coefficients, Fourier series of functions with special properties, special Fourier series (42A16) Nondifferentiability (nondifferentiable functions, points of nondifferentiability), discontinuous derivatives (26A27) Weyl sums (11L15)

Related Items (14)

An Analytical Study of Flatness and Intermittency through Riemann's Nondifferentiable Functions ⋮ Lattice points ⋮ On the Evolution of the Vortex Filament Equation for Regular $M$-Polygons with Nonzero Torsion ⋮ Hybrid bounds on two-parametric families of Weyl sums along smooth curves ⋮ Multifractal behavior of polynomial Fourier series ⋮ Fractal solutions of dispersive partial differential equations on the torus ⋮ Intermittency of Riemann’s non-differentiable function through the fourth-order flatness ⋮ On the Hausdorff dimension of Riemann’s non-differentiable function ⋮ Some Fourier series with gaps ⋮ Some geometric properties of Riemann's non-differentiable function ⋮ Unnamed Item ⋮ Automorphic forms and differentiability properties ⋮ Geometric differentiability of Riemann's non-differentiable function ⋮ Inferring the smoothness of the autocorrelation function from that of the initial state

Cites Work

• Pointwise analysis of Riemann's ``nondifferentiable function
• The Differentiability of the Riemann Function at Certain Rational Multiples of &#960
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