Smoothing of the Singularities of Functions Whose Integrals over the Balls on a Sphere are Zero

Smoothing of the Singularities of Functions Whose Integrals over the Balls on a Sphere are Zero

We study functions defined on a sphere with prickled point whose integrals over all admissible “hemispheres” are equal to zero. A condition is established under which the point is a removable set for this class of functions. It is shown that this condition cannot be omitted or noticeably weakened....

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Veröffentlicht in:Ukrainian mathematical journal 2015-07, Vol.67 (2), p.314-322
Hauptverfasser: Volchkov, Vit. V., Savost’yanova, I. M.
Format: Artikel
Sprache:eng
Schlagworte:
Algebra
Analysis
Applications of Mathematics
Brief Communications
Geometry
Mathematics
Mathematics and Statistics
Statistics
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Beschreibung
Zusammenfassung:We study functions defined on a sphere with prickled point whose integrals over all admissible “hemispheres” are equal to zero. A condition is established under which the point is a removable set for this class of functions. It is shown that this condition cannot be omitted or noticeably weakened.
ISSN:0041-5995
1573-9376
DOI:10.1007/s11253-015-1081-5