Computational Methods and Function Theory 5 (2005), No. 2, 489--503
Copyright Heldermann Verlag 2005
Oleksiy Dovgoshey
aleksdov@mail.ru , Institute of Applied Mathematics and Mechanics, NAS of Ukraine, 74 Roze Luxemburg str., Donetsk, 83114, Ukraine.
Let G be a simply connected, bounded domain on the plane with the boundary Γ and let P(Γ) be a uniform closure of polynomials on Γ. It is shown that the Rudin-Carleson Theorem about analytic extensions from zero measure boundary sets is valid for P(Γ) if and only if G is a Carathéodory domain and ‾G does not separate the plane. These conditions are also equivalent to maximality of P(Γ) in C(Γ).
Keywords: Caratheodory domains, harmonic measure, polynomial approximation, peak sets, interpolation sets, maximal subalgebras.
MSC 2000: Primary 30E10; Secondary 46J15, 46E25.
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