On the rate of pointwise divergence of Fourier and wavelet series in \(L^p\)

DOI10.1016/j.jat.2005.10.003zbMath1096.42022OpenAlexW2036639098MaRDI QIDQ818461

Jean-Marie Aubry

Publication date: 20 March 2006

Published in: Journal of Approximation Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jat.2005.10.003

zbMATH Keywords

Hausdorff dimensionFourier serieswavelet seriesCarleson--Hunt theorempointwise divergence

Mathematics Subject Classification ID

Nontrigonometric harmonic analysis involving wavelets and other special systems (42C40) Convergence and divergence of series and sequences of functions (40A30) Convergence and absolute convergence of Fourier and trigonometric series (42A20)

Related Items (7)

A refinement of strong multiplicity one for spectra of hyperbolic manifolds ⋮ A Bridge Between Geometric Measure Theory and Signal Processing: Multifractal Analysis ⋮ Boundary multifractal behaviour for harmonic functions in the ball ⋮ Divergence of wavelet series: a multifractal analysis ⋮ Divergence of the mock and scrambled Fourier series on fractal measures ⋮ Multifractal analysis of the divergence of Fourier series: the extreme cases ⋮ Multifractal phenomena and packing dimension

Cites Work

• Local convergence for wavelet expansions
• Pointwise convergence of wavelet expansions
• Hyperbolic wavelet approximation
• On the pointwise regularity of functions in critical Besov spaces
• On the Gibbs phenomenon for wavelet expansions
• Gibbs phenomenon for wavelets
• On convergence and growth of partial sums of Fourier series
• POINTWISE CONVERGENCE OF FOURIER SERIES
• Ten Lectures on Wavelets
• Multifractal Formalism for Functions Part I: Results Valid For All Functions
• Sur les ensembles de divergence des séries trigonométriques
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