Fourier Inversion for Piecewise Smooth Functions in Several Variables

DOI10.2307/2160140zbMath0783.42009OpenAlexW4235938937MaRDI QIDQ4201628

Mark A. Pinsky

Publication date: 1 September 1993

Full work available at URL: https://doi.org/10.2307/2160140

zbMATH Keywords

Fourier transformDirichlet kernelGibbs phenomenonradial functionsBessel differential equationFourier inversionspherical Bessel functionspiecewise smooth functions in several variables

Mathematics Subject Classification ID

Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42B10) Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.) (42C10) Bessel and Airy functions, cylinder functions, ({}_0F_1) (33C10)

Related Items (10)

Fourier inversion of distributions supported by a hypersurface ⋮ Localization for Riesz means of Fourier expansions ⋮ The Kahane theorem for nonspherical partial sums of Fourier integrals ⋮ On the Pinsky phenomenon ⋮ On the localization of the Riesz means of multiple Fourier series of distributions ⋮ Dependence of the convergence domain of spectral expansions on the geometry of the set of discontinuity of the function being expanded ⋮ Matrix Fourier transforms for consistent mathematical models ⋮ Generalized Hardy identity and relations to Gibbs-Wilbraham and Pinsky phenomena ⋮ Localization and convergence of eigenfunction expansions ⋮ Spherical means, wave equations, and Hermite-Laguerre expansions

Cites Work

• Fourier series of radial functions in several variables
• Gibbs' phenomenon for Fourier-Bessel series
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