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

This article is cited in 4 scientific papers (total in 4 papers)

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
Received in April 2001

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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    Citing articles on Google Scholar: Russian citations, English citations
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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  mathnet  mathscinet  zmath
    2. J. E. Brennan, “Thomson's theorem on mean square polynomial approximation”, St. Petersburg Math. J., 17:2 (2006), 217–238  mathnet  crossref  mathscinet  zmath  elib
    3. Brennan J.E., “On a Conjecture of Mergelyan”, Journal of Contemporary Mathematical Analysis–Armenian Academy of Sciences, 43:6 (2008), 341–352  crossref  mathscinet  zmath  isi
    4. A. L. Volberg, V. Ya. Èiderman, “Non-homogeneous harmonic analysis: 16 years of development”, Russian Math. Surveys, 68:6 (2013), 973–1026  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
  •    . . .  Proceedings of the Steklov Institute of Mathematics
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