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Sbornik: Mathematics, 2000, Volume 191, Issue 8, Pages 1215–1231
DOI: https://doi.org/10.1070/sm2000v191n08ABEH000501 (Mi sm501) 		 
This article is cited in 2 scientific papers (total in 2 papers)

Cauchy's integral formula in domains of arbitrary connectivity

M. V. Samokhin

Moscow State University of Civil Engineering
English version PDF (233 kB) Citations (2)
References:
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DOI: https://doi.org/10.1070/sm2000v191n08ABEH000501
Abstract: It is shown that a straightforward generalization of Cauchy's integral formula is possible only in domains with boundary of finite length (in some sense or other). An example of a simply connected domain with boundary of infinite length is constructed such that for fairly general functionals on $H^\infty$ no extremal function (including the Ahlfors function) can be represented as a Cauchy potential.
Received: 15.09.1999 and 15.05.2000
Russian version:
Matematicheskii Sbornik, 2000, Volume 191, Number 8, Pages 113–130
DOI: https://doi.org/10.4213/sm501
Bibliographic databases:
UDC: 517.53
MSC: Primary 30E20; Secondary 46J15, 46J20
Language: English
Original paper language: Russian
Citation: M. V. Samokhin, “Cauchy's integral formula in domains of arbitrary connectivity”, Mat. Sb., 191:8 (2000), 113–130; Sb. Math., 191:8 (2000), 1215–1231
Citation in format AMSBIB
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    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Математический сборник - 1992–2005 Sbornik: Mathematics
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    Russian version PDF:230
    English version PDF:9
    References:59
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