On the convergence of Vilenkin-Fourier series

DOI10.1007/BF01903394zbMath0395.42012OpenAlexW2505606862MaRDI QIDQ4178027

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Publication date: 1979

Published in: Acta Mathematica Academiae Scientiarum Hungaricae (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01903394

zbMATH Keywords

Compact Abelian GroupDirichlet KernelCharacter SystemDescrete Cyclic GroupsDini-Lipschitz ConditionGeneralized Walsh SystemL1-ConvergenceVilenkin SystemVilenkin-Fourier Series

Mathematics Subject Classification ID

Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.) (42C10) Character groups and dual objects (43A40) (L^1)-algebras on groups, semigroups, etc. (43A20) Convergence of Fourier series and of inverse transforms (43A50)

Related Items (5)

An analogy of the Carleson-Hunt theorem with respect to Vilenkin systems ⋮ Norm convergence of double Fourier series on unbounded Vilenkin groups ⋮ On the Parseval equality and the Dini-Lipschitz condition with respect to the Vilenkin system ⋮ On the divergence of Vilenkin-Fourier series ⋮ Dini-Lipschitz test and convergence of Fourier series with respect to multiplicative systems

Cites Work

• Unnamed Item
• On \(L^p\)-norm convergence of series with respect to product systems
• Uniform convergence of Fourier series on groups. I
• Mean Convergence of Generalized Walsh-Fourier Series
• Verallgemeinerte Walsh—Fourierreihen. II

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