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On subharmonic continuation of subharmonic functions and separation of singularities of analytic functions. (Russian) Zbl 0803.31001
Yulmukhametov, R. S. (ed.), Studies in approximation theory. Collection of articles. Ufa: Institut Matematiki BNTs AN SSSR, 44-49 (1989).
We state the following particular case of the author’s main result. Let \(G\) be a finitely connected domain \(G\) in the complex plane \(\mathbb{C}\). Fix an arbitrary point in every bounded connected component of \(\mathbb{C}\setminus G\) and denote by \(G_ 0\) the set of all these points. Then any subharmonic function \(u\) in \(G\) can be extended from any compact set \(K\subset G\) to the subharmonic function on \(\mathbb{C}\setminus G_ 0\).
As a corollary the author proves a variant of the Aronszajn’s theorem about separation of singularities of analytic functions.
For the entire collection see [Zbl 0742.00053].
31A05 Harmonic, subharmonic, superharmonic functions in two dimensions
30E99 Miscellaneous topics of analysis in the complex plane