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Mathematics of the USSR-Sbornik, 1987, Volume 57, Issue 2, Pages 463–483
DOI: https://doi.org/10.1070/SM1987v057n02ABEH003081 (Mi sm1840) 		 
This article is cited in 18 scientific papers (total in 18 papers)

Semigroups of conformal mappings

V. V. Goryainov
English version PDF (1159 kB) Citations (18) Russian version article
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DOI: https://doi.org/10.1070/SM1987v057n02ABEH003081
Abstract: Sets of conformal mappings distinguished by boundary conditions and forming semigroups with respect to the operation of composition are studied.
A description of one-parameter semigroups is given, and a connection between them and semiflows is established. With each semigroup there is associated an evolution equation that is an analogue of the Lëwner equation known in the theory of univalent functions. Existence theorems are obtained for the evolution equations, and their approximation properties are studied. It is also established that each mapping of the semigroups under consideration can be represented as a shift along solutions of the corresponding evolution equation.
Bibliography: 19 titles.
Received: 03.06.1985
Bibliographic databases:
UDC: 517.54
MSC: Primary 30C35; Secondary 30C50, 30C55, 35K22, 54H15
Language: English
Original paper language: Russian
Citation: V. V. Goryainov, “Semigroups of conformal mappings”, Math. USSR-Sb., 57:2 (1987), 463–483
Citation in format AMSBIB
\Bibitem{Gor86}
\by V.~V.~Goryainov
\paper Semigroups of conformal mappings
\jour Math. USSR-Sb.
\yr 1987
\vol 57
\issue 2
\pages 463--483
\mathnet{http://mi.mathnet.ru//eng/sm1840}
\crossref{https://doi.org/10.1070/SM1987v057n02ABEH003081}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=842395}
\zmath{https://zbmath.org/?q=an:0618.30009|0609.30009}
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    		Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics
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