Uniformly convergent Fourier series with universal power parts on closed subsets of measure zero

DOI10.1016/j.jat.2023.105864OpenAlexW4315642805MaRDI QIDQ2683696

Sergey Khrushchev

Publication date: 14 February 2023

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

Full work available at URL: https://doi.org/10.1016/j.jat.2023.105864

zbMATH Keywords

convergence of Fourier seriesFourier seriescontinuous functionsuniversal Fourier series

Mathematics Subject Classification ID

Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Theorems of Hahn-Banach type; extension and lifting of functionals and operators (46A22) Banach algebras of differentiable or analytic functions, (H^p)-spaces (46J15) (H^p)-spaces (42B30) Convergence and absolute convergence of Fourier and trigonometric series (42A20) Banach spaces of continuous, differentiable or analytic functions (46E15) Harmonic analysis on Euclidean spaces (42-XX) Approximations and expansions (41-XX)

Cites Work

• A Rudin-Carleson theorem for uniformly convergent Taylor series
• On universality and convergence of the Fourier series of functions in the disc algebra
• A continuous function with universal Fourier series on a given closed set of Lebesgue measure zero
• On convergence and growth of partial sums of Fourier series
• Functions of Vanishing Mean Oscillation
• Sur les ensembles de divergence des séries trigonométriques
• Sur les ensembles de divergence des séries trigonométriques
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