On the L1-convergence and behavior of coefficients of Fourier-Vilenkin series

DOI10.1007/s11117-018-0552-yzbMath1440.42132OpenAlexW2782607812MaRDI QIDQ1670449

Martin G. Grigoryan, Stepan Sargsyan

Publication date: 5 September 2018

Published in: Positivity (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11117-018-0552-y

zbMATH Keywords

convergenceVilenkin systemsFourier coefficients

Mathematics Subject Classification ID

Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.) (42C10) Fourier coefficients, Fourier series of functions with special properties, special Fourier series (42A16) Other transformations of harmonic type (42C20)

Cites Work

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• On \(L_p\)-convergence of Cesàro means for Fourier series with monotonic coefficients
• On the Fourier-Vilenkin coefficients
• On the existence of universal series by trigonometric system
• On null-series by double Walsh system
• Walsh series and adjustment of functions on small sets
• Modifications of functions, Fourier coefficients and nonlinear approximation
• Certain Groups of Orthonormal Step Functions
• On generalized Walsh Fourier series, I
• Greedy approximation with respect to certain subsystems of the Walsh orthonormal system
• Mean Convergence of Generalized Walsh-Fourier Series
• On the representation of functions by orthogonal series in weighted $L^p$ spaces
• On the $ L^p_\mu$-strong property of orthonormal systems
• ON CONVERGENCE OF FOURIER SERIES IN COMPLETE ORTHONORMAL SYSTEMS IN THE $ L^1$-METRIC AND ALMOST EVERYWHERE
• Almost Everywhere Convergence of Vilenkin-Fourier Series
• On a class of complete orthonormal systems
• Sur la convergence presque partout des séries de Fourier-Walsh des fonctions de l'espace L²(0,1)

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