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Funktsional. Anal. i Prilozhen., 2016, Volume 50, Issue 1, Pages 67–75 (Mi faa3224)  

This article is cited in 10 scientific papers (total in 10 papers)

Commuting Differential Operators of Rank 2 with Polynomial Coefficients

V. S. Oganesyan

Lomonosov Moscow State University

Abstract: Self-adjoint commuting differential operators with polynomial coefficients are considered. These operators form a commutative subalgebra of the first Weyl algebra. New examples of commuting differential operators of rank $2$ are found.

Keywords: differential operator, first Weyl algebra, Krichever–Novikov equation, Dixmier hypothesis, nonlinear equation, operator of nontrivial rank

Funding Agency Grant Number
Ministry of Education and Science of the Russian Federation НШ-4833.2014.1


DOI: https://doi.org/10.4213/faa3224

Full text: PDF file (150 kB)
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English version:
Functional Analysis and Its Applications, 2016, 50:1, 54–61

Bibliographic databases:

UDC: 517.926+512.77
Received: 20.02.2015

Citation: V. S. Oganesyan, “Commuting Differential Operators of Rank 2 with Polynomial Coefficients”, Funktsional. Anal. i Prilozhen., 50:1 (2016), 67–75; Funct. Anal. Appl., 50:1 (2016), 54–61

Citation in format AMSBIB
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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. S. Oganesyan, “On operators of the form $\partial_x^4+u(x)$ from a pair of commuting differential operators of rank 2 and genus $g$”, Russian Math. Surveys, 71:3 (2016), 591–593  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  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. D. A. Pogorelov, A. B. Zheglov, “An algorithm for construction of commuting ordinary differential operators by geometric data”, Lobachevskii J. Math., 38:6 (2017), 1075–1092  crossref  mathscinet  zmath  isi  scopus
    4. V. N. Davletshina, A. E. Mironov, “On commuting ordinary differential operators with polynomial coefficients corresponding to spectral curves of genus two”, Bull. Korean. Math. Soc., 54:5 (2017), 1669–1675  crossref  mathscinet  isi  scopus
    5. V. Oganesyan, “Explicit characterization of some commuting differential operators of rank 2”, Int. Math. Res. Not. IMRN, 2017, no. 6, 1623–1640  crossref  mathscinet  isi  scopus
    6. V. S. Oganesyan, “Commuting Differential Operators of Rank 2 with Rational Coefficients”, Funct. Anal. Appl., 52:3 (2018), 203–213  mathnet  crossref  crossref  isi  elib
    7. V. S. Oganesyan, “Alternative proof of Mironov's results on commuting self-adjoint operators of rank 2”, Siberian Math. J., 59:1 (2018), 102–106  mathnet  crossref  crossref  isi  elib
    8. 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
    9. Oganesyan V., “Matrix Commuting Differential Operators of Rank 2 and Arbitrary Genus”, Int. Math. Res. Notices, 2019, no. 3, 834–851  crossref  isi
    10. Emma Previato, Sonia L. Rueda, Maria-Angeles Zurro, “Commuting Ordinary Differential Operators and the Dixmier Test”, SIGMA, 15 (2019), 101, 23 pp.  mathnet  crossref
  • Функциональный анализ и его приложения Functional Analysis and Its Applications
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