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

• Date: 2015
• Main Authors: Volchkov, V. V., Savost’yanova, I. M., Волчков, Вит. В., Савостьянова, И. М.
• Format: Article
• Language: Russian; English
• Published: Institute of Mathematics, NAS of Ukraine 2015
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/1979
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

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....