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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© Pleiades Publishing, Ltd. 2017

Authors and Affiliations

  1. 1.Faculty of Mechanics and MathematicsMoscow State UniversityMoscowRussia
  2. 2.Bauman Moscow State Technical UniversityMoscowRussia

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