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Uspekhi Mat. Nauk, 2008, Volume 63, Issue 4(382), Pages 3–42 (Mi umn9230)  

This article is cited in 6 scientific papers (total in 6 papers)

Various versions of the Riemann–Hilbert problem for linear differential equations

R. R. Gontsova, V. A. Poberezhnyib

a Institute for Information Transmission Problems, Russian Academy of Sciences
b Institute for Theoretical and Experimental Physics (Russian Federation State Scientific Center)

Abstract: A counterexample to Hilbert's 21st problem was found by Bolibrukh in 1988 (and published in 1989). In the further study of this problem he substantially developed the approach using holomorphic vector bundles and meromorphic connections. Here the best-known results of the past that were obtained by using this approach (both for Hilbert's 21st problem and for certain generalizations) are presented.

DOI: https://doi.org/10.4213/rm9230

Full text: PDF file (846 kB)
References: PDF file   HTML file

English version:
Russian Mathematical Surveys, 2008, 63:4, 603–639

Bibliographic databases:

UDC: 517.927.7+517.936
MSC: Primary 34M50; Secondary 34M35, 34M55
Received: 30.06.2008

Citation: R. R. Gontsov, V. A. Poberezhnyi, “Various versions of the Riemann–Hilbert problem for linear differential equations”, Uspekhi Mat. Nauk, 63:4(382) (2008), 3–42; Russian Math. Surveys, 63:4 (2008), 603–639

Citation in format AMSBIB
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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. I. V. V'yugin, “On Hilbert's 21st problem for scalar Fuchsian equations”, Dokl. Math., 79:2 (2009), 203–206  mathnet  crossref  mathscinet  zmath  isi  elib  scopus
    2. D. V. Anosov, V. P. Leksin, “Andrei Andreevich Bolibrukh's works on the analytic theory of differential equations”, Russian Math. Surveys, 66:1 (2011), 1–33  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    3. I. V. Vyugin, “Riemann–Hilbert problem for scalar Fuchsian equations and related problems”, Russian Math. Surveys, 66:1 (2011), 35–62  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    4. A. A. Matveeva, V. A. Poberezhnyi, “The One-Dimensional Riemann Problem on an Elliptic Curve”, Math. Notes, 101:1 (2017), 115–122  mathnet  crossref  crossref  mathscinet  isi  elib
    5. Matveeva A.A., Poberezhny V.A., “Two-dimensional Riemann problem for rigid representations on an elliptic curve”, J. Geom. Phys., 114 (2017), 384–393  crossref  mathscinet  zmath  isi  scopus
    6. Bibilo Yu., Filipuk G., “Constructive Solutions to the Riemann–Hilbert Problem and Middle Convolution”, J. Dyn. Control Syst., 23:1 (2017), 55–70  crossref  mathscinet  zmath  isi  scopus
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