Remarks on the uniform and \(L^1\)-convergence of trigonometric series

DOI10.1007/S10474-010-9217-4zbMath1240.42015OpenAlexW2032089841MaRDI QIDQ625998

Péter Kórus

Publication date: 25 February 2011

Published in: Acta Mathematica Hungarica (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10474-010-9217-4

zbMATH Keywords

monotonicityuniform convergenceFourier series\(L^1\)-convergencesine seriesgeneral monotonesupremum bounded variation

Mathematics Subject Classification ID

Convergence and absolute convergence of Fourier and trigonometric series (42A20) Trigonometric series of special types (positive coefficients, monotonic coefficients, etc.) (42A32)

Related Items (9)

Uniform convergence of double sine transforms of general monotone functions ⋮ A sufficient condition for uniform convergence of trigonometric series with \(p\)-bounded variation coefficients ⋮ On the uniform convergence of special sine integrals ⋮ On \(L^1\)-convergence of Fourier series of complex valued functions under the \(GM_7\) condition ⋮ On the uniform convergence of single and double sine series ⋮ \(L^1\)-approximation rate of certain trigonometric series ⋮ On the uniform convergence of double sine series with generalized monotone coefficients ⋮ Approximation theory for sine series with coefficient from class supremum bounded variation sequences ⋮ A necessary condition for uniform convergence of double sine series with $p$-bounded variation coefficients

Cites Work

• Ultimate generalization to monotonicity for uniform convergence of trigonometric series
• On \(L_1\)-convergence of Fourier series
• A generalization of the monotonicity condition and applications

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