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New criteria for uniform approximability by harmonic functions on compact sets in ℝ2

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Abstract

New uniform approximability criteria formulated in terms of logarithmic capacity are obtained for approximations by harmonic functions on compact sets in ℝ2. A relationship between these approximations and analogous approximations on compact sets in ℝ3 is established.

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Authors and Affiliations

  1. Faculty of Mechanics and Mathematics, Moscow State University, Moscow, 119991, Russia

    P. V. Paramonov

  2. Bauman Moscow State Technical University, Vtoraya Baumanskaya ul. 5/1, Moscow, 105005, Russia

    P. V. Paramonov

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  1. P. V. Paramonov
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Correspondence to P. V. Paramonov.

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Original Russian Text © P.V. Paramonov, 2017, published in Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2017, Vol. 298, pp. 216–226.

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Paramonov, P.V. New criteria for uniform approximability by harmonic functions on compact sets in ℝ2 . Proc. Steklov Inst. Math. 298, 201–211 (2017). https://doi.org/10.1134/S0081543817060141

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  • DOI: https://doi.org/10.1134/S0081543817060141

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