Runge- and Walsh-type extensions of smooth subharmonic functions on open Riemann surfacesстатья
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Дата последнего поиска статьи во внешних источниках: 12 января 2017 г.
Аннотация:Abstract. In this paper we study several settings of the Cm-subharmonic
extension problem on open Riemann surfaces. The problem is completely
solved (for all m ∈ [0,+∞)) 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 Cm-subharmonic extensions, automorphic with
respect to some appropriate groups of automorphisms of an open Riemann
surface.
Bibliography: 22 titles.