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Sbornik: Mathematics, 2018, Volume 209, Issue 9, Pages 1376–1389
DOI: https://doi.org/10.1070/SM8969 (Mi sm8969) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Carathéodory sets and analytic balayage of measures

K. Yu. Fedorovskiyab

a Bauman Moscow State Technical University
b Saint Petersburg State University
English version PDF (498 kB) Citations (1) Russian version article
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DOI: https://doi.org/10.1070/SM8969
Abstract: We consider the concept of an analytic balayage of measures introduced by D. Khavinson. New formulae for analytic balayage are obtained in the case when the support of a measure lies inside some Carathéodory compact set, and balayage onto its boundary is considered. The constructions are based on recent results on the boundary behaviour of conformal mappings of the unit disc onto Carathéodory domains.
Bibliography: 27 titles.
Keywords: Carathéodory domain, Carathéodory compact set, orthogonal measure, analytic balayage, conformal mapping.
Funding agency Grant number
Ministry of Education and Science of the Russian Federation 1.517.2016/1.4
1.3843.2017/4.6
Russian Foundation for Basic Research 16-01-00674-а
17-51-150005-НЦНИ_а
Simons Foundation Simons-IUM fellowship
The research was supported by the Ministry of Education and Science of the Russian Federation (project nos. 1.517.2016/1.4 and 1.3843.2017/4.6). The work was also supported by the Russian Foundation for Basic Research (project nos. 16-01-00674-a and 17-51-150005-НЦНИ-a) and the Simons Foundation (Simons-IUM fellowship).
Received: 18.05.2017 and 19.06.2018
Bibliographic databases:
Document Type: Article
UDC: 517.53
MSC: Primary 30E10; Secondary 41A30, 41A50, 30C20
Language: English
Original paper language: Russian
Citation: K. Yu. Fedorovskiy, “Carathéodory sets and analytic balayage of measures”, Sb. Math., 209:9 (2018), 1376–1389
Citation in format AMSBIB
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\by K.~Yu.~Fedorovskiy
\paper Carath\'eodory sets and analytic balayage of measures
\jour Sb. Math.
\yr 2018
\vol 209
\issue 9
\pages 1376--1389
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  • https://doi.org/10.1070/SM8969
  • https://www.mathnet.ru/eng/sm/v209/i9/p128
    • This publication is cited in the following 1 articles:
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