A Note on Rational Approximation with Respect to Metrizable Compactifications of the Plane
Palabras clave:
compactification, Arakelian’s theorem, Mergelyan’s theorem, Runge’s theorem, uniform approximation in the complex domain.Resumen
In the present note we examine possible extensions of Runge, Mergelyan and Arakelian Theorems, when the uniform approximation is meant with respect to the metric ρ of a metrizable compactification (S, ρ) of the complex plane C.
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Referencias
I. Androulidakis, V. Nestoridis, Extension of the disc algebra and of Mergelyan’s theorem, C.R. Math. Acad. Sci. Paris 349 (13–14) (2011), 745 – 748.
N.U. Arakelian, Uniform approximation on closed sets by entire functions, Izv. Akad. Nauk SSSR Ser. Mat. 28 (1964), 1187 – 1206 (Russian).
L. Brown, P.M. Gauthier, W. Hengartner, Continuous boundary behaviour for functions defined in the open unit disc, Nagoya Math. J. 57 (1975), 49 – 58.
G. Costakis, V. Nestoridis, I. Papadoperakis, Universal Laurent series, Proc. Edinb. Math. Soc. (2) 48 (3) (2005), 571 – 583.
M. Fragoulopoulou, V. Nestoridis, I. Papadoperakis, Some results on spherical approximation, Bull. Lond. Math. Soc. 45 (6) (2013), 1171 – 1180.
V. Nestoridis, Compactifications of the plane and extensions of the disc algebra, in “ Complex Analysis and Potential Theory ” , CRM Proc. Lecture Notes, 55, Amer. Math. Soc., Providence, RI, 2012, 61 – 75.
V. Nestoridis, An extension of the disc algebra, I, Bull. Lond. Math. Soc. 44 (4) (2012), 775 – 788.
V. Nestoridis, N. Papadatos, An extension of the disc algebra, II, Complex Var. Elliptic Equ. 59 (7) (2014), 1003 – 1015.
V. Nestoridis, I. Papadoperakis, A remark on two extensions of the disc algebra and Mergelian’s theorem, preprint 2011, arxiv: 1104.0833.
W. Rudin, “ Real and Complex Analysis ”, McGraw-Hill Book Co., New York- Toronto, Ont.-London, 1966.