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


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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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P. Paramonov

Faculty of Mechanics and Mathematics; Bauman Moscow State Technical University

Autor responsável pela correspondência
Email: petr.paramonov@list.ru
Rússia, Moscow, 119991; Vtoraya Baumanskaya ul. 5/1, Moscow, 105005

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