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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.
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
Linking options:
https://www.mathnet.ru/eng/sm501https://doi.org/10.1070/sm2000v191n08ABEH000501 https://www.mathnet.ru/eng/sm/v191/i8/p113
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Abstract page: | 465 | Russian version PDF: | 230 | English version PDF: | 9 | References: | 59 | First page: | 1 |
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