Inversion of fractional integrals related to the spherical Radon transform

DOI10.1006/jfan.1998.3268zbMath0910.42006OpenAlexW2006898107MaRDI QIDQ1268070

Boris Rubin

Publication date: 12 April 1999

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

Full work available at URL: https://doi.org/10.1006/jfan.1998.3268

zbMATH Keywords

Beltrami-Laplace operatorRadon transformsanalytical continuationfractional integralsspherical convolutionsspherical Fourier multiplier

Mathematics Subject Classification ID

Multipliers for harmonic analysis in several variables (42B15) Fractional derivatives and integrals (26A33) Radon transform (44A12)

Related Items

Liouville theorems for a general class of nonlocal operators, Funk-Minkowski transform and spherical convolution of Hilbert type in reconstructing functions on the sphere, Comparison of volumes of convex bodies in real, complex, and quaternionic spaces, The lower dimensional Busemann-Petty problem for bodies with the generalized axial symmetry, Funk, cosine, and sine transforms on Stiefel and Grassmann manifolds, Intersection bodies and generalized cosine transforms, The Cos\(^\lambda\) and Sin\(^\lambda\) transforms as intertwining operators between generalized principal series representations of SL\((n+1,\mathbb K)\), Fractional integrals and wavelet transforms associated with Blaschke-Lévy representations on the sphere, On Complex L_p affine isoperimetric inequalities, Composite Cosine Transforms, Inversion and characterization of the hemispherical transform, 𝐿_{𝑝}-Blaschke valuations, The \(d\)-plane Radon transform on the torus \(\mathbb T^n\), Inversion formulas for the spherical Radon transform and the generalized cosine transform.

Cites Work

• Centrally symmetric convex bodies and the spherical Radon transform
• Generalized Riesz potentials and hypersingular integrals with homogeneous characteristics, their symbols and inversion
• The Radon transform
• Spherical Radon transform and related wavelet transforms
• Inversion of \(k\)-plane transforms via continuous wavelet transforms
• Inversion of Radon transforms using wavelet transforms generated by wavelet measures
• Radon transform of Lp -functions on the Lobachevsky space and hyperbolic wavelet transforms
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