A Runge theorem for harmonic functions on closed subsets of Riemann surfaces
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- by Thomas Bagby PDF
- Proc. Amer. Math. Soc. 103 (1988), 160-164 Request permission
Abstract:
Let $F$ be a closed subset of a Riemann surface $\Omega$. It is shown that every function which is harmonic on a neighborhood of $F$ can be uniformly approximated on $F$ by functions which are harmonic on $\Omega$ except for poles.References
- A. Boivin and P. M. Gauthier, Approximation harmonique sur les surfaces de Riemann, Canad. J. Math. 36 (1984), no. 1, 1–8 (French). MR 733703, DOI 10.4153/CJM-1984-001-2
- A. Dufresnoy, P. M. Gauthier, and W. H. Ow, Uniform approximation on closed sets by solutions of elliptic partial differential equations, Complex Variables Theory Appl. 6 (1986), no. 2-4, 235–247. MR 871732, DOI 10.1080/17476938608814171
- P. M. Gauthier, M. Goldstein, and W. H. Ow, Uniform approximation on unbounded sets by harmonic functions with logarithmic singularities, Trans. Amer. Math. Soc. 261 (1980), no. 1, 169–183. MR 576870, DOI 10.1090/S0002-9947-1980-0576870-5
- P. M. Gauthier and W. Hengartner, Uniform approximation on closed sets by functions analytic on a Riemann surface, Approximation theory (Proc. Conf. Inst. Math., Adam Mickiewicz Univ., Poznań, 1972) Reidel, Dordrecht, 1975, pp. 63–69. MR 0486540
- Paul M. Gauthier and Walter Hengartner, Approximation uniforme qualitative sur des ensembles non bornés, Séminaire de Mathématiques Supérieures [Seminar on Higher Mathematics], vol. 82, Presses de l’Université de Montréal, Montreal, Que., 1982 (French). MR 658131
- L. Sario and M. Nakai, Classification theory of Riemann surfaces, Die Grundlehren der mathematischen Wissenschaften, Band 164, Springer-Verlag, New York-Berlin, 1970. MR 0264064
- R. Narasimhan, Analysis on real and complex manifolds, North-Holland Mathematical Library, vol. 35, North-Holland Publishing Co., Amsterdam, 1985. Reprint of the 1973 edition. MR 832683
Additional Information
- © Copyright 1988 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 103 (1988), 160-164
- MSC: Primary 30F15; Secondary 30E10
- DOI: https://doi.org/10.1090/S0002-9939-1988-0938662-7
- MathSciNet review: 938662