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Inversion Formulas for Integral Operations of Weighted Plane Wave Type

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We obtain the inversion formula for Newton B-potentials with Hӧlder densities. If the weight exponent is a natural number, the weighted plane waves are represented via spherical transformations of integral operations with plane waves. The inversion formulas for integral operations with kernel are presented by the action of the Poisson operator on some power of the inner product of vectors.

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Authors and Affiliations

  1. Voronezh State University, 1, Universitetskaya pl., Voronezh, 394006, Russia

    L. N. Lyakhov

  2. Lipetsk State Pedagogical University, 42, Lenina St., Lipetsk, 398020, Russia

    M. G. Lapshina

Authors
  1. L. N. Lyakhov
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  2. M. G. Lapshina
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Correspondence to L. N. Lyakhov.

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Translated from Problemy Matematicheskogo Analiza 84, April 2016, pp. 113-121.

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Lyakhov, L.N., Lapshina, M.G. Inversion Formulas for Integral Operations of Weighted Plane Wave Type. J Math Sci 216, 270–278 (2016). https://doi.org/10.1007/s10958-016-2900-4

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  • DOI: https://doi.org/10.1007/s10958-016-2900-4

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