Some problems in the theory of approximation of functions on locally compact Vilenkin groups

DOI10.1134/S2070046619020067zbMath1430.43002OpenAlexW2943220534WikidataQ114074757 ScholiaQ114074757MaRDI QIDQ2281430

Sergei S. Platonov

Publication date: 19 December 2019

Published in: \(p\)-Adic Numbers, Ultrametric Analysis, and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s2070046619020067

zbMATH Keywords

modulus of continuityembedding theoremsLipschitz conditionapproximation of functionslocally compact Vilenkin groupszero-dimensional groups

Mathematics Subject Classification ID

Nontrigonometric harmonic analysis involving wavelets and other special systems (42C40) (L^p)-spaces and other function spaces on groups, semigroups, etc. (43A15) Numerical methods in Fourier analysis (65T99)

Related Items

Step wavelets on Vilenkin groups, Fourier transform of Dini-Lipschitz functions on locally compact Vilenkin groups, Ulyanov-type embedding theorems for functions on zero-dimensional locally compact groups, Fourier transform of Dini-Lipschitz functions on the field of \(p\)-adic numbers, Embedding theorems for Hölder classes defined on \(p\)-adic linear spaces

Cites Work

• Hausdorff operators on \(p\)-adic linear spaces and their properties in Hardy, \(BMO\), and Hölder spaces
• On the orthogonality of a system of shifts of the scaling function on Vilenkin groups
• Biorthogonal wavelets on Vilenkin groups
• On the modulus of continuity with respect to functions defined on Vilenkin groups
• Moduli of continuity of functions, defined on a zero-dimensional group
• Hörmander-type multipliers on locally compact Vilenkin groups: the \(L^1(G)\)-case
• Some problems in the theory of approximation of functions on the group of \(p\)-adic numbers
• An analogue of the Titchmarsh theorem for the Fourier transform on locally compact Vilenkin groups
• Wavelet frames on Vilenkin groups and their approximation properties
• Fourier Analysis on Local Fields. (MN-15)
• Multipliers of weak type on locally compact Vilenkin groups
• Harmonic Analysis and Fractal Analysis over Local Fields and Applications
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