Free interpolation and Dirichlet problem
Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part XIII, Tome 135 (1984), pp. 51-65

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A compact subset $K$ of the closed upper half-plane $\mathbb C_+\cup\mathbb R$ is called a Dirichlet set if every function continuous on $K$ is the restriction of a function continuous in $\mathbb C_+\cup\mathbb R$ and harmonic in $\mathbb C_+$. A description of Dirichlet sets is given.
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     author = {A. O. Derviz and V. P. Havin},
     title = {Free interpolation and {Dirichlet} problem},
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     year = {1984},
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     url = {http://geodesic.mathdoc.fr/item/ZNSL_1984_135_a3/}
}
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A. O. Derviz; V. P. Havin. Free interpolation and Dirichlet problem. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part XIII, Tome 135 (1984), pp. 51-65. http://geodesic.mathdoc.fr/item/ZNSL_1984_135_a3/