The Riemann‐Hilbert problem for finite riemann surfaces
1959; Wiley; Volume: 12; Issue: 1 Linguagem: Inglês
10.1002/cpa.3160120103
ISSN1097-0312
Autores Tópico(s)Mathematical Analysis and Transform Methods
ResumoCommunications on Pure and Applied MathematicsVolume 12, Issue 1 p. 13-35 Article The Riemann-Hilbert problem for finite riemann surfaces† Walter Koppelman, Walter Koppelman Yale UniversitySearch for more papers by this author Walter Koppelman, Walter Koppelman Yale UniversitySearch for more papers by this author First published: February 1959 https://doi.org/10.1002/cpa.3160120103Citations: 35 † This paper is based on the author's doctoral dissertation, submitted to the faculty of New York University. The author wishes to express his gratitude to Professor L. Bers for his suggestions and encouragement. AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Bibliography 1 Behnke, H., and Sommer, F., Theorie der analytischen Funktionen, Springer, Berlin, 1955. 2 Bers, L., An outline of the theory of pseudoanalytic functions, Bull. Amer. Math. Soc., Vol. 62, 1956, pp. 291– 331. 3 Danilyuk, I. I., On the integral representation of solutions of certain elliptic systems of the first order on surfaces and their use in the theory of thin shells, Doklady Akad. Nauk SSSR, N. S., Vol. 109, 1956, pp. 17– 20. 4 Hilbert, D., Über eine Anwendung der Integralgleichungen auf ein Problem der Funktionentheorie, Verh. d. III. Intern. Kongr., Heidelberg, 1904. 5 Hilbert, D., Grundzüge einer allgemeinen Theorie der linearen Integralgleichungen, B. G. Teubner, Leipzig, 1912. 6 Kellogg, O. D., Harmonic functions and Green's integral, Trans. Amer. Math. Soc., Vol. 13, 1912, pp. 109– 132. 7 Kveselava, D. A., The Riemann-Hilbert problem for multiply connected domains, Soobšč. Akad. Nauk Gruzin. SSR, Vol. 6, 1945, pp. 581– 590. 8 Muskhelishvili, N. I., Singular Integral Equations; Boundary Problems of Function Theory and Their Application to Mathematical Physics, P. Noordhoff, Groningen, 1933. (Translated from the Russian.) 9 Nevanlinna, R., Uniformisierung, Springer, Berlin, 1953. 10 Nitsche, J., Untersuchungen über die linearen Randwertprobleme linearer und quasilinearer elliptischer Differentialgleichungssysteme, Math. Nachr., Vol. 14, 1955, pp. 75– 127, 157–182. 11 Noether, F., Über eine Klasse singulärer Integralgleichungen, Math. Ann., Vol. 82, 1921, pp. 42– 63. 12 Riemann, B., Grundlagen für eine allgemeine Theorie der Funktionen einer veränderlichen komplexen Grösse, Werke, Leipzig, 1876, pp. 3– 43. 13 Schiffer, M., and Spencer, D. C., Functionals of Finite Riemann Surfaces, Princeton Univ. Press., 1954. 14 Seifert, H., and Threlfall, W., Lehrbuch der Topologie, B. G. Teubner, Berlin, 1934. 15 Vekua, I. N., Systems of partial differential equations of first order of elliptic type and boundary value problems with applications to the theory of shells, Mat. Sbornik, N. S., Vol. 31, 1952, pp. 217– 314. 16 Warschawski, S., Über das Randverhalten der Ableitung der Abbildungsfunktion bei konformer Abbildung, Math. Z., Vol. 35, 1932, pp. 321– 456. 17 Weyl, H., Die Idee der Riemannschen Fläche, B. G. Teubner, Stuttgart, 1955. 18 Hopf, E., A remark on linear elliptic differential equations of the second order, Proc. Amer. Math. Soc., Vol. 3, 1952, pp. 791– 793. Citing Literature Volume12, Issue1February 1959Pages 13-35 ReferencesRelatedInformation
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