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The Clifford theorem for quasirational functions. (English. Russian original) Zbl 0995.30027

Russ. Math. 43, No. 4, 7-11 (1999); translation from Izv. Vyssh. Uchebn. Zaved., Mat. 1999, No. 4, 9-13 (1999).
Es wird folgende Verallgemeinerung des klassischen Cliffordschen Theorems bewiesen: Sei \(R\) eine parabolische Riemannsche Fläche vom Genus \(h \leq \infty\) und sei \(D\) ein Divisor auf \(R\) mit \(0\leq\text{ord} D\leq 2h-1\). Sei \(\ell\) die Dimension des Raumes aller quasirationaler Funktionen, multipel zu \(1/D\). Dann gilt \(\ell\leq [\text{ord} D/2]+1\).

MSC:

30F10 Compact Riemann surfaces and uniformization
Full Text: DOI

References:

[1] L. I. Chibrikova, ”Boundary-Value Problems of the Theory of Analytic Functions on Riemann Surfaces,” in Itogi Nauki i Tekhniki. Matem. Analiz (VINITI, 1980), Vol. 18, pp. 3–66.
[2] E.I. Zverovich, ”Boundary-Value Problems in the Theory of Analytic Functions in Hölder Classes on Riemann Surfaces,” Usp. Mat. Nauk 26(1), 113–179 (1971). · Zbl 0217.10201
[3] I. A. Bikchantaev, ”Riemann Problem on a Finite-Sheeted Riemann Surface of Infinite Genus,” Matem. Zametki 67(1), 25–35 (2000). · Zbl 0970.30024
[4] A. P. Soldatov, One-Dimensional Singular Operators and Boundary-Value Problems of Function. Theory (Vysshaya Shkola, Moscow, 1991 ) [in Russian].
[5] L. Sario and M. Nakai, Classification Theory of Open Riemann Surfaces (Springer-Verlag, Berlin-Heidelberg-New York, 1970). · Zbl 0199.40603
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