The Behnke-Stein theorem for open Riemann surfaces
HTML articles powered by AMS MathViewer
- by R. R. Simha PDF
- Proc. Amer. Math. Soc. 105 (1989), 876-880 Request permission
Abstract:
Using the Riemann-Roch theorem and the set-topological part of Bishop’s special polyhedron lemma, we show that the usual Runge approximation theorem for compact subsets of the Riemann sphere is valid word-for-word on any compact Riemann surface $X$, with meromorphic functions on $X$ playing the role of rational functions; this result is essentially equivalent to the Behnke-Stein approximation theorem.References
- Heinrich Behnke and Karl Stein, Entwicklung analytischer Funktionen auf Riemannschen Flächen, Math. Ann. 120 (1949), 430–461 (German). MR 29997, DOI 10.1007/BF01447838
- Errett Bishop, Mappings of partially analytic spaces, Amer. J. Math. 83 (1961), 209–242. MR 123732, DOI 10.2307/2372953
- Stanisław Saks and Antoni Zygmund, Analytic functions, Monografie Matematyczne, Tom XXVIII, Polskie Towarzystwo Matematyczne, Warszawa-Wroclaw, 1952. Translated by E. J. Scott. MR 0055432
Additional Information
- © Copyright 1989 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 105 (1989), 876-880
- MSC: Primary 30E10; Secondary 30F10
- DOI: https://doi.org/10.1090/S0002-9939-1989-0953748-X
- MathSciNet review: 953748