An analogue of the Titchmarsh theorem for the Fourier transform on locally compact Vilenkin groups

DOI10.1134/S2070046617040057zbMath1388.43004OpenAlexW2766643428MaRDI QIDQ1743665

Sergei S. Platonov

Publication date: 13 April 2018

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

Full work available at URL: https://doi.org/10.1134/s2070046617040057

zbMATH Keywords

Fourier transformmodulus of continuityVilenkin groupsTitchmarsh theoremharmonic analysis on Vilenkin groups

Mathematics Subject Classification ID

Fourier and Fourier-Stieltjes transforms on locally compact and other abelian groups (43A25) Measure algebras on groups, semigroups, etc. (43A10)

Related Items (8)

Yang-Fourier transforms of Lipschitz local fractional continuous functions ⋮ Mellin transform of log-Lipschitz functions and equivalence of \(K\)-functionals and modulus of smoothness generated by the Mellin Steklov operator ⋮ Fourier transform of Dini-Lipschitz functions on locally compact Vilenkin groups ⋮ Wavelet transform of Dini Lipschitz functions on the quaternion algebra ⋮ Some problems in the theory of approximation of functions on locally compact Vilenkin groups ⋮ Octonion Fourier transform of Lipschitz real-valued functions of three variables on the octonion algebra ⋮ Decay of Fourier Transforms and Generalized Besov Spaces ⋮ Some new estimates concerning the Mellin transform on the space \(X_c^2\)

Cites Work

• On the orthogonality of a system of shifts of the scaling function on Vilenkin groups
• Biorthogonal wavelets 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
• Fourier transforms of Lipschitz functions on the hyperbolic plane \(H^2\)
• An analogue of the Titchmarsh theorem for the Fourier transform on the group of \(p\)-adic numbers
• An analog of Titchmarsh's Theorem for the Dunkl transform
• 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
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