Geodesic
New Criteria for Uniform Approximability by Harmonic Functions on Compact Sets in $\mathbb R^2$
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Complex analysis and its applications, Tome 298 (2017), pp. 216-226

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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 $\mathbb R^2$. A relationship between these approximations and analogous approximations on compact sets in $\mathbb R^3$ is established.
Keywords: uniform approximation by harmonic functions, Vitushkin-type localization operator, harmonic capacity, logarithmic capacity, reduction method. 
@article{TM_2017_298_a13,
     author = {P. V. Paramonov},
     title = {New {Criteria} for {Uniform} {Approximability} by {Harmonic} {Functions} on {Compact} {Sets} in $\mathbb R^2$},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {216--226},
     publisher = {mathdoc},
     volume = {298},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2017_298_a13/}
}
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P. V. Paramonov. New Criteria for Uniform Approximability by Harmonic Functions on Compact Sets in $\mathbb R^2$. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Complex analysis and its applications, Tome 298 (2017), pp. 216-226. http://geodesic.mathdoc.fr/item/TM_2017_298_a13/