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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2017, Number 8, Pages 17–26 (Mi ivm9265)  
The extension problem for functions with zero weighted spherical means

Vit. V. Volchkova, N. P. Volchkovab

a Donetsk National University, 24 Universitetskaya str., Donetsk, 83001 Ukraine
b Donetsk National Technical University, 58 Artema str., Donetsk, 83000 Ukraine
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Abstract: 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.
Received: 28.03.2016
Revised: 31.07.2016
English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2017, Volume 61, Issue 8, Pages 13–21
DOI: https://doi.org/10.3103/S1066369X17080023
Bibliographic databases:
Document Type: Article
UDC: 517.444
Language: Russian
Citation: Vit. V. Volchkov, N. P. Volchkova, “The extension problem for functions with zero weighted spherical means”, Izv. Vyssh. Uchebn. Zaved. Mat., 2017, no. 8, 17–26; Russian Math. (Iz. VUZ), 61:8 (2017), 13–21
Citation in format AMSBIB
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