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Mat. Sb. (N.S.), 1980, Volume 113(155), Number 2(10), Pages 263–284 (Mi msb2791)  

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


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.

Full text: PDF file (1018 kB)
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English version:
Mathematics of the USSR-Sbornik, 1982, 41:2, 217–234

Bibliographic databases:

UDC: 517.9
MSC: Primary 35A10, 35B65, 35B60, 35C15; Secondary 32A25, 42B10
Received: 18.12.1979

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/msb2791}
\mathscinet{http://www.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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    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. B. Yu. Sternin, V. E. Shatalov, “On a method of solving equations with simple characteristics”, Math. USSR-Sb., 44:1 (1983), 23–59  mathnet  crossref  mathscinet  zmath
    2. Shatalov V., “Asymptotic Solutions of a Complex-Analytic Characteristic Cauchy-Problem”, 273, no. 2, 1983, 309–312  mathscinet  zmath  isi
    3. Sternin B., Shatalov V., “The Contact Geometry and Linear-Differential Equations”, 1108, 1984, 257–277  mathscinet  zmath  isi
    4. Sternin B., Shatalov V., “Some Integral Transformations of Complex Analytic-Functions”, 280, no. 3, 1985, 553–556  mathscinet  zmath  isi
    5. B. Yu. Sternin, V. E. Shatalov, “On an integral transform of complex analytic functions”, Math. USSR-Izv., 29:2 (1987), 407–427  mathnet  crossref  mathscinet  zmath
    6. Sternin B., Shatalov V., “Singularities of Differential-Equations on Complex-Analytic Manifolds”, 292, no. 5, 1987, 1058–1062  mathscinet  zmath  isi
    7. B. Yu. Sternin, V. E. Shatalov, “Differential equations on complex-analytic manifolds, and the Maslov canonical operator”, Russian Math. Surveys, 43:3 (1988), 117–148  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    8. B. Yu. Sternin, V. E. Shatalov, “Asymptotics of solutions of differential equations on complex varieties”, Math. USSR-Sb., 65:2 (1990), 385–422  mathnet  crossref  mathscinet  zmath
    9. Khavinson D., Lundberg E., “The Search for Singularities of Solutions to the Dirichlet Problem: Recent Developments”, Hilbert Spaces of Analytic Functions, CRM Proceedings & Lecture Notes, 51, eds. Mashreghi J., Ransford T., Seip K., Amer Mathematical Soc, 2010, 121–132  mathscinet  zmath  isi
    10. Lundberg E., “Laplacian Growth, Elliptic Growth, and Singularities of the Schwarz Potential”, J. Phys. A-Math. Theor., 44:13 (2011), 135202  crossref  mathscinet  zmath  adsnasa  isi  elib
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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