Comparison of V- and S-Dini tests. Counterexamples for symmetric Dini tests with respect to generalized Haar and Walsh systems

DOI10.3103/S1066369X1909007XzbMath1442.42066OpenAlexW2987685797WikidataQ125052877 ScholiaQ125052877MaRDI QIDQ2191551

Victor Shcherbakov

Publication date: 25 June 2020

Published in: Russian Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3103/s1066369x1909007x

zbMATH Keywords

abelian groupgeneralized Haar systemsVilenkin groupDirichlet kernelsprice systemsDini testcharacter systems

Mathematics Subject Classification ID

Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.) (42C10) Convergence and absolute convergence of Fourier and trigonometric series (42A20)

Cites Work

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• Divergence of the Fourier series by generalized Haar systems at points of continuity of a function
• Pointwise convergence of Fourier series with respect to multiplicative systems
• Convergence of series with respect to generalized Haar systems
• Majorants of the Dirichlet kernels and the Dini pointwise tests for generalized Haar systems
• A class of generalized Walsh functions
• Certain Groups of Orthonormal Step Functions
• A Remarkable Series of Orthogonal Functions (I)
• Graphs with Contours in Multiresolution Analysis on Vilenkin Groups
• Dini – Lipschitz Test on the Generalized Haar Systems
• On the Walsh Functions

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