Divergence of the mock and scrambled Fourier series on fractal measures

DOI10.1090/S0002-9947-2013-06021-7zbMath1406.42008arXiv1103.4380MaRDI QIDQ5401758

Dorin Ervin Dutkay, Qiyu Sun, De Guang Han

Publication date: 12 March 2014

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1103.4380

zbMATH Keywords

Hilbert spaceiterated function systemHadamard matrixDirichlet kernelFourier seriesfractalselfsimilar

Mathematics Subject Classification ID

Fractals (28A80) Fourier series and coefficients in several variables (42B05)

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Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On the rate of pointwise divergence of Fourier and wavelet series in \(L^p\)
• Fourier frequencies in affine iterated function systems
• Dense analytic subspaces in fractal \(L^2\)-spaces
• Decreasing rearranged Fourier series
• Mock Fourier series and transforms associated with certain Cantor measures
• On spectral Cantor measures
• Divergence of decreasing rearranged Fourier series
• Affine systems: asymptotics at infinity for fractal measures
• Convergence of mock Fourier series
• On uniformly convergent rearrangements of trigonometric Fourier series
• On convergence and growth of partial sums of Fourier series
• Iterated function systems, Ruelle operators, and invariant projective measures
• An ergodic theorem for iterated maps
• Self-Similar Sets 5. Integer Matrices and Fractal Tilings of ℝ n
• Convergence of greedy approximation II. The trigonometric system
• Sur les ensembles de divergence des séries trigonométriques
• Pointwise convergence of Fourier series

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