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.
English version (Springer): Ukrainian Mathematical Journal 67 (2015), no. 2, pp 314-322.
Citation Example: Savost’yanova I. M., Volchkov V. V. Smoothing of the Singularities of Functions Whose Integrals over the Balls on a Sphere are Zero // Ukr. Mat. Zh. - 2015. - 67, № 2. - pp. 272-278.