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

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Ukrainian Mathematical Journal Aims and scope

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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Authors and Affiliations

  1. Donetsk National University, Donetsk, Ukraine

    Vit. V. Volchkov & I. M. Savost’yanova

Authors
  1. Vit. V. Volchkov
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  2. I. M. Savost’yanova
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 67, No. 2, pp. 272–278, February, 2015.

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Volchkov, V.V., Savost’yanova, I.M. Smoothing of the Singularities of Functions Whose Integrals over the Balls on a Sphere are Zero. Ukr Math J 67, 314–322 (2015). https://doi.org/10.1007/s11253-015-1081-5

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  • DOI: https://doi.org/10.1007/s11253-015-1081-5

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