Geodesic
Runge- and Walsh-type extensions of smooth subharmonic functions on open Riemann surfaces
Sbornik. Mathematics, Tome 206 (2015) no. 1, pp. 3-23
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In this paper we study several settings of the $C^m$-subharmonic extension problem on open Riemann surfaces. The problem is completely solved (for all $m\in[0,+\infty)$) for so-called Runge-type extensions. Several (in some sense sharp) sufficient conditions and counterexamples are found also for Walsh-type extensions. As applications, these results allow us to prove the existence of $C^m$-subharmonic extensions, automorphic with respect to some appropriate groups of automorphisms of an open Riemann surface. Bibliography: 22 titles.
Keywords: subharmonic function, Riemann surface, Green function, localization operator
Mots-clés : automorphism group. 
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A. Boivin; P. M. Gauthier; P. V. Paramonov. Runge- and Walsh-type extensions of smooth subharmonic functions on open Riemann surfaces. Sbornik. Mathematics, Tome 206 (2015) no. 1, pp. 3-23. http://geodesic.mathdoc.fr/item/SM_2015_206_1_a1/

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