Abstract
A compact set K in the closed upper half plane
is called a Dirichlet set if any continuous function on K can be extended to a harmonic function in
, continuous in
. A description of Dirichlet sets is given.
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Additional information
Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 135, pp. 51–65, 1984.
We are grateful to A. B. Aleksandrov and N. A. Shirokov for helpful adivce.
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Derviz, A.O., Khavin, V.P. Free interpolation and the Dirichlet problem. J Math Sci 31, 2672–2680 (1985). https://doi.org/10.1007/BF02107249
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DOI: https://doi.org/10.1007/BF02107249