Geodesic
The extension problem for functions with zero weighted spherical means
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 8 (2017), pp. 17-26

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We study functions on a sphere with pricked point having zero integrals with a given weight over all admissible “hemispheres”. We find a condition under which a point is the removable set for such class of functions. We show that this condition cannot be dropped or substantially weakened.
Keywords: spherical harmonics, generalized Funk transform, mean periodicity. 
@article{IVM_2017_8_a1,
     author = {Vit. V. Volchkov and N. P. Volchkova},
     title = {The extension problem for functions with zero weighted spherical means},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {17--26},
     publisher = {mathdoc},
     number = {8},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2017_8_a1/}
}
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Vit. V. Volchkov; N. P. Volchkova. The extension problem for functions with zero weighted spherical means. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 8 (2017), pp. 17-26. http://geodesic.mathdoc.fr/item/IVM_2017_8_a1/