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Mathematics of the USSR-Sbornik, 1982, Volume 41, Issue 2, Pages 217–234
DOI: https://doi.org/10.1070/SM1982v041n02ABEH002230 (Mi sm2791) 		 
This article is cited in 10 scientific papers (total in 10 papers)

Legendre uniformization of multi-valued analytic functions

B. Yu. Sternin, V. E. Shatalov
English version PDF (1148 kB) Citations (10)
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DOI: https://doi.org/10.1070/SM1982v041n02ABEH002230
Abstract: In the first part of this article, the notion of Legendre uniformization of a multi-valued analytic function is introduced. This is a global generalization of the Leray uniformization, and consists in representing the function as an integral of Feynman type naturally associated with a certain Legendre manifold.
In the second part of the article, a transformation of Fourier type is defined for a certain class of uniformized functions, and an inversion formula is proved. Also, some natural commutation relations with differentiations and multiplications by the independent variables are established.
Bibliography: 11 titles.
Received: 18.12.1979
Russian version:
Matematicheskii Sbornik. Novaya Seriya, 1980, Volume 113(155), Number 2(10), Pages 263–284
Bibliographic databases:
UDC: 517.9
MSC: Primary 35A10, 35B65, 35B60, 35C15; Secondary 32A25, 42B10
Language: English
Original paper language: Russian
Citation: B. Yu. Sternin, V. E. Shatalov, “Legendre uniformization of multi-valued analytic functions”, Mat. Sb. (N.S.), 113(155):2(10) (1980), 263–284; Math. USSR-Sb., 41:2 (1982), 217–234
Citation in format AMSBIB
\Bibitem{SteSha80}
\by B.~Yu.~Sternin, V.~E.~Shatalov
\paper Legendre uniformization of multi-valued analytic functions
\jour Mat. Sb. (N.S.)
\yr 1980
\vol 113(155)
\issue 2(10)
\pages 263--284
\mathnet{http://mi.mathnet.ru/sm2791}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=594838}
\zmath{https://zbmath.org/?q=an:0517.35004|0498.35005}
\transl
\jour Math. USSR-Sb.
\yr 1982
\vol 41
\issue 2
\pages 217--234
\crossref{https://doi.org/10.1070/SM1982v041n02ABEH002230}
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  • https://www.mathnet.ru/eng/sm/v155/i2/p263
    • This publication is cited in the following 10 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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    Abstract page:394
    Russian version PDF:118
    English version PDF:16
    References:61
     
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