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Izv. Akad. Nauk SSSR Ser. Mat., 1986, Volume 50, Issue 3, Pages 458–478 (Mi izv1497)  

This article is cited in 5 scientific papers (total in 5 papers)

Vector rank of commuting matrix differential operators. Proof of S. P. Novikov's criterion

P. G. Grinevich


Abstract: The problem of describing a commuting pair of differential operators in terms of its Burchnall–Chaundy curve and the holomorphic bundle over it is considered. A characteristic of the matrix case is the occurrence of vector rank, a bundle having various dimensions over various components of the Burchnall–Chaundy curve. A complete, independent system which determines the pair of operators uniquely is chosen. In the last section, a proof is given of S. P. Novikov's criterion for an operator with periodic coefficients to be an operator of a nontrivial commuting pair.
Bibliography: 25 titles.

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English version:
Mathematics of the USSR-Izvestiya, 1987, 28:3, 445–465

Bibliographic databases:

UDC: 517.43
MSC: 47E05, 34B25
Received: 21.02.1984

Citation: P. G. Grinevich, “Vector rank of commuting matrix differential operators. Proof of S. P. Novikov's criterion”, Izv. Akad. Nauk SSSR Ser. Mat., 50:3 (1986), 458–478; Math. USSR-Izv., 28:3 (1987), 445–465

Citation in format AMSBIB
\Bibitem{Gri86}
\by P.~G.~Grinevich
\paper Vector rank of commuting matrix differential operators. Proof of S.\,P.~Novikov's criterion
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1986
\vol 50
\issue 3
\pages 458--478
\mathnet{http://mi.mathnet.ru/izv1497}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=854592}
\zmath{https://zbmath.org/?q=an:0623.47049|0609.47061}
\transl
\jour Math. USSR-Izv.
\yr 1987
\vol 28
\issue 3
\pages 445--465
\crossref{https://doi.org/10.1070/IM1987v028n03ABEH000892}


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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. A. Taimanov, “Secants of Abelian varieties, theta functions, and soliton equations”, Russian Math. Surveys, 52:1 (1997), 147–218  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    2. I. M. Krichever, S. P. Novikov, “Two-dimensionalized Toda lattice, commuting difference operators, and holomorphic bundles”, Russian Math. Surveys, 58:3 (2003), 473–510  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    3. A. B. Zheglov, A. E. Mironov, “Moduli Beikera – Akhiezera, puchki Krichevera i kommutativnye koltsa differentsialnykh operatorov v chastnykh proizvodnykh”, Dalnevost. matem. zhurn., 12:1 (2012), 20–34  mathnet
    4. A. B. Zheglov, “Surprising examples of nonrational smooth spectral surfaces”, Sb. Math., 209:8 (2018), 1131–1154  mathnet  crossref  crossref  adsnasa  isi  elib
    5. V. S. Oganesyan, “The AKNS hierarchy and finite-gap Schrödinger potentials”, Theoret. and Math. Phys., 196:1 (2018), 983–995  mathnet  crossref  crossref  adsnasa  isi  elib
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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