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Uspekhi Mat. Nauk, 2016, Volume 71, Issue 4(430), Pages 155–184 (Mi umn9730)  

This article is cited in 1 scientific paper (total in 1 paper)

Self-adjoint commuting differential operators of rank two

A. E. Mironov

Sobolev Mathematical Institute, Siberian Branch of the Russian Academy of Sciences

Abstract: This is a survey of results on self-adjoint commuting ordinary differential operators of rank two. In particular, the action of automorphisms of the first Weyl algebra on the set of commuting differential operators with polynomial coefficients is discussed, as well as the problem of constructing algebro-geometric solutions of rank $l>1$ of soliton equations.
Bibliography: 59 titles.

Keywords: commuting differential operators of rank two, self-adjoint operators, Weyl algebra.

Funding Agency Grant Number
Russian Foundation for Basic Research 15-01-01671-а
Dynasty Foundation
This paper was written with the support of the Russian Foundation for Basic Research (grant no. 15-01-01671-a) and Dmitry Zimin's "Dynasty" foundation.


DOI: https://doi.org/10.4213/rm9730

Full text: PDF file (709 kB)
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English version:
Russian Mathematical Surveys, 2016, 71:4, 751–779

Bibliographic databases:

UDC: 517.984+512.77
MSC: 34L40, 13N10, 14H70, 37K20
Received: 04.06.2016

Citation: A. E. Mironov, “Self-adjoint commuting differential operators of rank two”, Uspekhi Mat. Nauk, 71:4(430) (2016), 155–184; Russian Math. Surveys, 71:4 (2016), 751–779

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. E. L. Shishkina, S. M. Sitnik, “On fractional powers of Bessel operators”, J. Inequal. Spec. Funct., 8:1 (2017), 49–67  mathscinet  isi  elib
  • Успехи математических наук Russian Mathematical Surveys
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