Generalized Hardy identity and relations to Gibbs-Wilbraham and Pinsky phenomena

DOI10.1016/J.JFA.2010.03.025zbMath1200.42004OpenAlexW2006465730MaRDI QIDQ977490

Shigehiko Kuratsubo, Eiichi Nakai, Kazuya Ootsubo

Publication date: 22 June 2010

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jfa.2010.03.025

zbMATH Keywords

Fourier transformindicator functionFourier seriesGibbs-Wilbraham phenomenonHardy's identityLattice point problemPinsky phenomenonSpherical partial sumVoronoi-Hardy's identity

Mathematics Subject Classification ID

Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42B10) Fourier series and coefficients in several variables (42B05) Summability in several variables (42B08)

Related Items (2)

Biographical Sketch of Professor Eiichi Nakai ⋮ Multiple Fourier series and lattice point problems

Cites Work

• Fourier series of radial functions in several variables
• Localization and convergence of eigenfunction expansions
• On pointwise convergence of Fourier series of the Indicator function of \(D\) dimensional ball
• Fourier Inversion for Piecewise Smooth Functions in Several Variables
• On pointwise convergence of Fourier series of radial functions in several variables
• Pointwise fourier inversion and related eigenfunction expansions
• On lattice points in higher-dimensional ellipsoids
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