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This article is cited in 3 scientific papers (total in 3 papers)
Real, complex and functional analysis
Funk–Minkowski transform and spherical convolution of Hilbert type in reconstructing functions on the sphere
S. G. Kazantsev Sobolev Institute of Mathematics,
4, pr. Koptyuga,
Novosibirsk, 630090, Russia
Abstract:
The Funk–Minkowski transform ${\mathcal F}$ associates a function $f$ on the sphere ${\mathbb S}^2$ with its mean values (integrals) along all great circles of the sphere. The presented analytical inversion formula reconstruct the unknown function $f$ completely if two Funk–Minkowski transforms, ${\mathcal F}f$ and ${\mathcal F} \nabla f$, are known. Another result of this article is related to the problem of Helmholtz–Hodge decomposition for tangent vector field on the sphere ${\mathbb S}^2$. We proposed solution for this problem which is used the Funk–Minkowski transform ${\mathcal F}$ and Hilbert type spherical convolution ${\mathcal S}$.
Keywords:
Funk–Minkowski transform, Funk–-Radon transform, spherical convolution of Hilbert type, Fourier multiplier operator, inverse operator, surface gradient, scalar and vector spherical harmonics, tangential spherical vector field, Helmholtz–Hodge decomposition.
Received July 4, 2018, published December 14, 2018
Citation:
S. G. Kazantsev, “Funk–Minkowski transform and spherical convolution of Hilbert type in reconstructing functions on the sphere”, Sib. Èlektron. Mat. Izv., 15 (2018), 1630–1650
Linking options:
https://www.mathnet.ru/eng/semr1024 https://www.mathnet.ru/eng/semr/v15/p1630
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Abstract page: | 220 | Full-text PDF : | 112 | References: | 16 |
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