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 Tr. Mat. Inst. Steklova, 2001, Volume 235, Pages 157–164 (Mi tm241)

Saga of the Painlevé Problem and Analytic Capacity

M. S. Mel'nikov

Abstract: This note consists of two sections. The first one gives an account of an intriguing and dramatic story of solving (not completely) the so-called Painlevé problem that consists in describing the set of removable singularities for bounded holomorphic functions. In view of this, I indulge in proposing some reminiscences about bygone events. The second section gives yet another elementary proof of the Denjoy conjecture, which is a part of the Painlevé problem.

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English version:
Proceedings of the Steklov Institute of Mathematics, 2001, 235, 150–157

Bibliographic databases:
UDC: 517.5

Citation: M. S. Mel'nikov, “Saga of the Painlevé Problem and Analytic Capacity”, Analytic and geometric issues of complex analysis, Collected papers. Dedicated to the 70th anniversary of academician Anatolii Georgievich Vitushkin, Tr. Mat. Inst. Steklova, 235, Nauka, MAIK «Nauka/Inteperiodika», M., 2001, 157–164; Proc. Steklov Inst. Math., 235 (2001), 150–157

Citation in format AMSBIB
\Bibitem{Mel01} \by M.~S.~Mel'nikov \paper Saga of the Painlev\'e Problem and Analytic Capacity \inbook Analytic and geometric issues of complex analysis \bookinfo Collected papers. Dedicated to the 70th anniversary of academician Anatolii Georgievich Vitushkin \serial Tr. Mat. Inst. Steklova \yr 2001 \vol 235 \pages 157--164 \publ Nauka, MAIK «Nauka/Inteperiodika» \publaddr M. \mathnet{http://mi.mathnet.ru/tm241} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=1886580} \zmath{https://zbmath.org/?q=an:1003.30019} \transl \jour Proc. Steklov Inst. Math. \yr 2001 \vol 235 \pages 150--157 

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This publication is cited in the following articles:
1. K. Yu. Fedorovskiy, “Approximation and Boundary Properties of Polyanalytic Functions”, Proc. Steklov Inst. Math., 235 (2001), 251–260
2. J. E. Brennan, “Thomson's theorem on mean square polynomial approximation”, St. Petersburg Math. J., 17:2 (2006), 217–238
3. Brennan J.E., “On a Conjecture of Mergelyan”, Journal of Contemporary Mathematical Analysis–Armenian Academy of Sciences, 43:6 (2008), 341–352
4. A. L. Volberg, V. Ya. Èiderman, “Non-homogeneous harmonic analysis: 16 years of development”, Russian Math. Surveys, 68:6 (2013), 973–1026
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