Funk-Minkowski transform and spherical convolution of Hilbert type in reconstructing functions on the sphere

DOI10.33048/semi.2018.15.135zbMath1422.42008arXiv1806.06672OpenAlexW3015438690MaRDI QIDQ2633490

Sergeĭ Gavrilovich Kazantsev

Publication date: 9 May 2019

Published in: Sibirskie Èlektronnye Matematicheskie Izvestiya (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1806.06672

zbMATH Keywords

inverse operatorHelmholtz-Hodge decompositionFourier multiplier operatorsurface gradientFunk-Radon transformFunk-Minkowski transformscalar and vector spherical harmonicsspherical convolution of Hilbert typetangential spherical vector field

Mathematics Subject Classification ID

Differential geometric aspects in vector and tensor analysis (53A45) Radon transform (44A12) Integral geometry (53C65) Multipliers in one variable harmonic analysis (42A45) Classical operational calculus (44A45)

Related Items (4)

A discrete Funk transform on the cubed sphere ⋮ On two families of Funk-type transforms ⋮ Reconstruction of functions on the sphere from their integrals over hyperplane sections ⋮ Singular value decomposition of the longitudinal ray transform of vector fields in a ball in cone beam coordinates

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