References
Appel, P.: Sur les fonctions uniformes d'un point analytique I, II, and Développements en série dans une aire limitée par des arcs de cercle. Acta Math.1, 109–131, 132–144, and 145–152 (1883)
Arakelyan, N.U.: Uniform approximation on closed sets by entire functions [Russian], Akad. Nauk SSSR, Izvestia, ser. mat.28, 1187–1206 (1964)
Arakelyan, N.U.: Approximation complexe et propriétés des fonctions analytiques. Actes, Congrès intern. Math.2, 595–600 (1970)
Bishop, E.: Subalgebras of functions on a Riemann surface. Pacific J. Math.8, 29–50 (1968)
Bishop, E.: The structure of certain measures. Duke Math. J.25, 283–289 (1958)
Bishop, E.: Boundary measures of analytic differentials. Duke Math. J.27, 332–340 (1960)
Behnke, H., Sommer, F.: Theorie der analytischen Funktionen eines Komplexen Veränderlichen, pp. 581–592, 2. Aufl. Berlin, Göttingen, Heidelberg: Springer 1962
Behnke, H., Stein, K.: Entwicklung analytischer Funktionen auf Riemannschen Flächen. Math. Ann.120, 430–461 (1949)
Gamelin, T.W.: Uniform algebras. Chap. II. Englewood Cliffs: Prentice-Hall 1969
Gauthier, P.M.: Meromorphic uniform approximation on closed subsets of open Riemann surfaces. In: Proceedings of the Brasil Conference on Approximation and Holomorphy. Prolia, J.B., ed. 1978
Kodama, L.K.: Boundary measures of analytic differentials and uniform approximation on a Riemann surface. Pacific J. Math.15, 1261–1277 (1965)
Keldyš, M.V., Lavrentiev, M.A.: Sur un problème de M. Carleman. C.R. (Doklady) Acad. Sci. USSR (N.S.)23, 746–748 (1939)
Köditz, H., Timmann, S.: Randschlichte meromorphe Funktionen auf endlichen Riemannschen Flächen. Math. Ann.217, 157–159 (1975)
Mergelyan, S.N.: Uniform approximations to functions of a complex variable. Amer. Math. Soc. Transl. Ser. 1,3, 294–391 (1964)
Roth, A.: Uniform and tangential approximations by meromorphic functions on closed sets. Can. J. Math.28, 104–111 (1976)
Rodin, B., Sario, L.: Principal functions, p. 205. Princeton: van Nostrand 1968
Rudin, W.: Real and complex analysis. 2nd Ed. New York: McGraw-Hill 1974
Runge, C.: Zur Theorie der analytischen Funktionen und Entwicklung der Wurzeln einer algebraischen Gleichung in Summen von rationalen Funktionen der Koeffizienten. Acta Math.6, 245–248 and 305–318 (1885)
Scheinberg, S.: Uniform approximation by functions analytic on a Riemann surface. Ann. of Math.108, 257–298 (1978)
Springer, G.: Introduction to Riemann surfaces. London: Addison-Wesley 1957
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Partially supported by NSF Grant MCS77-01848
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Scheinberg, S. Uniform approximation by meromorphic functions having prescribed poles. Math. Ann. 243, 83–93 (1979). https://doi.org/10.1007/BF01420209
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DOI: https://doi.org/10.1007/BF01420209