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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].
MSC:
 31A05 Harmonic, subharmonic, superharmonic functions in two dimensions 30E99 Miscellaneous topics of analysis in the complex plane