On the convergence of the rotated one-sided ergodic Hilbert transform

DOI10.1007/s11117-010-0070-zzbMath1228.47013OpenAlexW2090255260MaRDI QIDQ548202

Guy Cohen, Jean-Pierre Conze, Nicolas Chevallier

Publication date: 28 June 2011

Published in: Positivity (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11117-010-0070-z

zbMATH Keywords

Hausdorff dimensionspectral measurecontractionsone-sided rotated ergodic Hilbert transform

Mathematics Subject Classification ID

Ergodic theory of linear operators (47A35) Hermitian and normal operators (spectral measures, functional calculus, etc.) (47B15) Ergodic theorems, spectral theory, Markov operators (37A30) Fourier coefficients, Fourier series of functions with special properties, special Fourier series (42A16)

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On the rate of convergence of weighted oscillating ergodic averages ⋮ Everywhere divergence of one-sided ergodic Hilbert transform ⋮ Weighted strong laws of large numbers on variable exponent vector-valued Lebesgue spaces ⋮ Weighted laws of large numbers and convergence of weighted ergodic averages on vector valued \(L_p\)-spaces

Cites Work

• A Wiener-Wintner theorem for the Hilbert transform
• On the a.s. convergence of the one-sided ergodic Hilbert transform
• On Random Fourier Series
• Spectral Criteria for Existence ofGeneralized Ergodic Transforms
• Wiener–Wintner dynamical systems
• Spectral characterization of WienerWintner dynamical systems
• Harmonic Analysis and Ergodic Theory
• A Non Homogeneous Ergodic Theorem
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