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Sibirsk. Mat. Zh., 2018, Volume 59, Number 1, Pages 130–135 (Mi smj2959)  

This article is cited in 2 scientific papers (total in 2 papers)

Alternative proof of Mironov's results on commuting self-adjoint operators of rank 2

V. S. Oganesyan

Lomonosov Moscow State University, Moscow, Russia

Abstract: We give an alternative proof of Mironov's results on commuting self-adjoint operators of rank 2. Mironov's proof is based on Krichever's complicated theory of the existence of a high-rank Baker–Akhiezer function. In contrast to Mironov's proof, our proof is simpler but the results are slightly weaker. Note that the method of this article can be extended to matrix operators. Using the method, we can construct the first explicit examples of matrix commuting differential operators of rank 2 and arbitrary genus.

Keywords: commuting differential operators.

Funding Agency Grant Number
Russian Science Foundation 16-11-10260
The research was carried out at the Department of Mechanics and Mathematics of Moscow State University and supported by the Russian Science Foundation (Grant 16-11-10260).


DOI: https://doi.org/10.17377/smzh.2018.59.111

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English version:
Siberian Mathematical Journal, 2018, 59:1, 102–106

Bibliographic databases:

UDC: 517.926
MSC: 35R30
Received: 24.04.2017

Citation: V. S. Oganesyan, “Alternative proof of Mironov's results on commuting self-adjoint operators of rank 2”, Sibirsk. Mat. Zh., 59:1 (2018), 130–135; Siberian Math. J., 59:1 (2018), 102–106

Citation in format AMSBIB
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\paper Alternative proof of Mironov's results on commuting self-adjoint operators of rank~2
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\yr 2018
\vol 59
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\pages 130--135
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\crossref{https://doi.org/10.17377/smzh.2018.59.111}
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\pages 102--106
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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. Emma Previato, Sonia L. Rueda, Maria-Angeles Zurro, “Commuting Ordinary Differential Operators and the Dixmier Test”, SIGMA, 15 (2019), 101, 23 pp.  mathnet  crossref
    2. Ya. H. Saleem, H. A. Shubber, “Essential self-adjointness of the Schrödinger operator with electromagnetic potential”, J. Interdiscip. Math., 22:8 (2019), 1537–1542  crossref  isi  scopus
  • Сибирский математический журнал Siberian Mathematical Journal
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