On the kernel of a hemispherical Funk transformation and its local analogs

DOI10.1007/S10958-014-1803-5zbMath1307.44007OpenAlexW2044604115MaRDI QIDQ460744

Vitalii Vladimirovich Volchkov, Irina M. Savost'yanova

Publication date: 14 October 2014

Published in: Journal of Mathematical Sciences (New York) (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10958-014-1803-5

zbMATH Keywords

spherical harmonicssymmetric spaceLegendre functionsintegral geometryconvolution equationPompeiu transformationhomogenous spacehemispherical Funk transformationhemispherical transformation

Mathematics Subject Classification ID

Convolution as an integral transform (44A35) Special integral transforms (Legendre, Hilbert, etc.) (44A15) Harmonic analysis on homogeneous spaces (43A85) Integral geometry (53C65) Harmonic analysis and spherical functions (43A90)

Cites Work

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• Pompeiu's problem on symmetric spaces
• Inversion and characterization of the hemispherical transform
• The Pompeiu problem on locally symmetric spaces
• Mean-value theorems for a class of polynomials
• Analog of the John theorem for weighted spherical means on a sphere
• Offbeat Integral Geometry on Symmetric Spaces
• Harmonic Analysis of Mean Periodic Functions on Symmetric Spaces and the Heisenberg Group
• Über eine Integralgleichung in der Theorie der konvexen Körper
• Freak Theorem About Functions on a Sphere

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