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An analogue of the Löwner equation for mappings of strips. (English. Russian original) Zbl 1154.30008

Russ. Math. 51, No. 8, 74-77 (2007); translation from Izv. Vyssh. Uchebn. Zaved., Mat. 2007, No. 8, 77-80 (2007).
An analogue of the Löwner equation for conformal mappings, defined on a strip, with finite angular derivatives the the infinite points is obtained.

MSC:

30C35 General theory of conformal mappings
30C55 General theory of univalent and multivalent functions of one complex variable
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References:

[1] K. Löwner, ”Untersuchungen über schlichte konforme Abbildungen des Einheitskreises. I”, Math. Ann. 89, 103–121 (1923). · JFM 49.0714.01
[2] V. V. Goryainov, ”Semigroups of Conformal Mappings,” Matem. Sborn. 129(4), 451–472 (1986). · Zbl 0609.30009
[3] S. Rohde and O. Schramm, ”Basic Properties of SLE,” Ann. Math. 161(2), 879–920 (2005). · Zbl 1081.60069
[4] P. L. Duren, Univalent Functions (Springer-Verlag, New York, 1983).
[5] V. V. Goryainov, ”Fractional Iterations of Analytic in the Unit Disc Functions with Given Fixed Points,” Matem. Sborn. 182(9), 1281–1299 (1991). · Zbl 0741.30019
[6] M. A. Lavrent’ev and B. V. Shabat, Methods of Theory of Functions of Complex Variable (Nauka, Moscow, 1973) [in Russian].
[7] N. Dunford and J. T. Schwartz, Linear Operators. General Theory (Interscience Publishers, New York, London, 1958; Inostr. Lit., Moscow, 1962).
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