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Sibirsk. Mat. Zh., 2014, Volume 55, Number 4, Pages 744–749 (Mi smj2568)  

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

On commuting differential operators of rank $2$

V. N. Davletshinaab, E. I. Shamaevac

a Sobolev Institute of Mathematics, Novosibirsk, Russia
b Novosibirsk State University, Novosibirsk, Russia
c Ammosov North-Eastern Federal University, Yakutsk, Russia

Abstract: We study examples of formally self-adjoint commuting ordinary differential operators of order $4$ or $4g+2$ whose coefficients are analytic on $\mathbb C$. We prove that these operators do not commute with the operators of odd order, justifying rigorously that these operators are of rank 2.

Keywords: commuting differential operator of rank 2.

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English version:
Siberian Mathematical Journal, 2014, 55:4, 606–610

Bibliographic databases:

Document Type: Article
UDC: 517.98
Received: 20.05.2014

Citation: V. N. Davletshina, E. I. Shamaev, “On commuting differential operators of rank $2$”, Sibirsk. Mat. Zh., 55:4 (2014), 744–749; Siberian Math. J., 55:4 (2014), 606–610

Citation in format AMSBIB
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\by V.~N.~Davletshina, E.~I.~Shamaev
\paper On commuting differential operators of rank~$2$
\jour Sibirsk. Mat. Zh.
\yr 2014
\vol 55
\issue 4
\pages 744--749
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\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3242592}
\transl
\jour Siberian Math. J.
\yr 2014
\vol 55
\issue 4
\pages 606--610
\crossref{https://doi.org/10.1134/S003744661404003X}
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\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84906494239}


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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. V. N. Davletshina, “Commuting differential operators of rank $2$ with trigonometric coefficients”, Siberian Math. J., 56:3 (2015), 405–410  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    2. A. E. Mironov, “Self-adjoint commuting differential operators of rank two”, Russian Math. Surveys, 71:4 (2016), 751–779  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    3. A. B. Zheglov, A. E. Mironov, B. T. Saparbayeva, “Commuting Krichever–Novikov differential operators with polynomial coefficients”, Siberian Math. J., 57:5 (2016), 819–823  mathnet  crossref  crossref  isi  elib  elib
    4. A. E. Mironov, A. B. Zheglov, “Commuting ordinary differential operators with polynomial coefficients and automorphisms of the first Weyl algebra”, Int. Math. Res. Notices, 2016, no. 10, 2974–2993  crossref  mathscinet  isi  scopus
  • Сибирский математический журнал Siberian Mathematical Journal
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