On radial functions and distributions and their Fourier transforms

DOI10.1007/s00041-013-9313-2zbMath1315.46045OpenAlexW1968864649MaRDI QIDQ485230

Ricardo Estrada

Publication date: 9 January 2015

Published in: The Journal of Fourier Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00041-013-9313-2

zbMATH Keywords

Fourier transformdistributionstempered distributionstest functions

Mathematics Subject Classification ID

Integral transforms in distribution spaces (46F12)

Related Items (12)

Diagonal spherical means ⋮ Weighted Hankel transform and its applications to Fourier transform ⋮ Distributional point values and delta sequences ⋮ Tauberian theorems for smooth functions that never vanish ⋮ Renormalization Group Circuits for Weakly Interacting Continuum Field Theories ⋮ Characterization of harmonic functions by the behavior of means at a single point ⋮ A note on recent papers by Grafakos and Teschl, and Estrada ⋮ Fourier transformation of \(O(p,q)\)-invariant distributions. Fundamental solutions of ultra-hyperbolic operators ⋮ Asymptotic expansion of thick distributions ⋮ Formal series on cylinders and their Radon transform ⋮ Unnamed Item ⋮ On the Fourier transform of rotationally invariant distributions

Cites Work

• On Fourier transforms of radial functions and distributions
• The nonexistence of regularization operators.
• Regularization and distributional derivatives of ( x ₁ ² + x ₂ ² + . . . + x _p ² ) ^{–½ n} in R ^p
• A Distributional Approach to Dual Integral Equations of Titchmarsh Type
• A Characterization of the Inverse Laplace Transforms of Rational Positive-Real Matrices
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