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Mat. Sb., 2000, Volume 191, Number 8, Pages 113–130 (Mi msb501)  

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

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.

DOI: https://doi.org/10.4213/sm501

Full text: PDF file (304 kB)
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English version:
Sbornik: Mathematics, 2000, 191:8, 1215–1231

Bibliographic databases:

UDC: 517.53
MSC: Primary 30E20; Secondary 46J15, 46J20
Received: 15.09.1999 and 15.05.2000

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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\by M.~V.~Samokhin
\paper Cauchy's integral formula in domains of arbitrary connectivity
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\vol 191
\issue 8
\pages 113--130
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\issue 8
\pages 1215--1231
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. S. Ya. Khavinson, “Duality relations in the theory of analytic capacity”, St. Petersburg Math. J., 15:1 (2004), 1–40  mathnet  crossref  mathscinet  zmath
    2. Younsi M., “On the Analytic and Cauchy Capacities”, J. Anal. Math., 135:1 (2018), 185–202  crossref  mathscinet  zmath  isi  scopus
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
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