Best conditions for the norm convergence of Fourier series

DOI10.1016/0021-9045(83)90152-1zbMath0516.42020OpenAlexW2016929329MaRDI QIDQ1052574

Paolo M. Soardi, Donald I. Cartwright

Publication date: 1983

Published in: Journal of Approximation Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0021-9045(83)90152-1

zbMATH Keywords

uniform convergencemodulus of continuitynorm convergenceHölder classFourier series over spheresFourier series over squaressymmetric space of rank 1

Mathematics Subject Classification ID

Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42B10) Harmonic analysis on specific compact groups (43A75) Summability and absolute summability of Fourier and trigonometric series (42A24) Best constants in approximation theory (41A44)

Related Items (11)

Fejér kernels for Fourier series on \(\mathbb{T}^ n\) and on compact Lie groups ⋮ Sharp Estimates for Lebesgue Constants ⋮ Lipschitz spaces on compact Lie groups ⋮ Sharp estimates for Lebesgue constants on compact Lie groups ⋮ Pointwise convergence of Fejér type means ⋮ Lebesgue Constants for Jacobi Expansions ⋮ Jackson's theorem for compact connected Lie groups ⋮ Estimates for Lebesgue constants in dimension two ⋮ On the asymptotics of the Bochner-Riesz kernel on compact Lie groups ⋮ Estimates for Riesz kernels of eigenfunction expansions of elliptic differential operators on compact manifolds ⋮ Hardy's inequality for certain compact homogeneous spaces

Cites Work

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• Sommes de Riesz et multiplicateurs sur un groupe de Lie compact
• Fourier series of differentiable functions on SU(2)
• The Lebesgue Constants for Jacobi Series, I
• Gaussian processes on compact symmetric spaces
• PROBLEMS OF CONVERGENCE OF MULTIPLE TRIGONOMETRIC SERIES AND SPECTRAL DECOMPOSITIONS. II
• Elementary spherical functions on symmetric spaces.
• Polynomial Approximation on Compact Manifolds and Homogeneous Spaces
• Introduction to Lie Algebras and Representation Theory

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