Universal Series on a Riemann Surface
Canadian journal of mathematics, Tome 63 (2011) no. 5, pp. 1025-1037

Voir la notice de l'article provenant de la source Cambridge University Press

Every holomorphic function on a compact subset of a Riemann surface can be uniformly approximated by partial sums of a given series of functions. Those functions behave locally like the classical fundamental solutions of the Cauchy–Riemann operator in the plane.
DOI : 10.4153/CJM-2011-013-x
Mots-clés : 30B60, 30E10, 30F99
Clouâtre, Raphäel. Universal Series on a Riemann Surface. Canadian journal of mathematics, Tome 63 (2011) no. 5, pp. 1025-1037. doi: 10.4153/CJM-2011-013-x
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[1] [1] Ahlfors, L. V. and Sario L. , Riemann surfaces. Princeton Mathematical Series, 26, Princeton University Press, Princeton, NJ, 1960. Google Scholar

[2] [2] Forster, O., Lectures on Riemann surfaces. Graduate Texts in Mathematics, 81, Springer-Verlag, New York-Berlin, 1981. Google Scholar

[3] [3] Gauthier, P. M., Mittag-Leffler theorems on Riemann surfaces and Riemannian manifolds. Canad. J. Math 50(1998), no. 3, 547–562. doi:10.4153/CJM-1998-030-1 Google Scholar

[4] [4] Grosse-Erdmann, K.-G., Universal families and hypercyclic operators. Bull. of Amer. Math. Soc 36(1999), no. 3, 345–381. doi:10.1090/S0273-0979-99-00788-0 Google Scholar

[5] [5] Gunning, R. C. and Narasimhan, R., Immersion of open Riemann surfaces. Math. Ann 174(1967), 103–108. doi:10.1007/BF01360812 Google Scholar

[6] [6] Hörmander, L., An introduction to complex analysis in several variables. D. Van Nostrand Co., Inc., Princeton, NJ-Toronto, ON-London, 1966. Google Scholar

[7] [7] Nestoridis, V. and Papadimitripopoulos, C., Abstract theory of universal series and an application to Dirichlet series. C. R. Acad. Sci. Paris 341(2005), no. 9, 539–543. Google Scholar

[8] [8] Stefanopoulos, V., Universal series and fundamental solutions of the Cauchy–Riemann Operator. Comput. Methods Funct. Theory 9(2009), no. 1, 1–12. Google Scholar

[9] [9] Tarkhanov, N. N., The Cauchy problem for solutions of elliptic equations. Akademie Verlag, Berlin, 1995. Google Scholar

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