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Sibirsk. Mat. Zh., 2016, Volume 57, Number 5, Pages 1048–1053 (Mi smj2805)  

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

Commuting Krichever–Novikov differential operators with polynomial coefficients

A. B. Zheglova, A. E. Mironovb, B. T. Saparbayevab

a Moscow State University, Moscow, Russia
b Sobolev Institute of Mathematics, Novosibirsk, Russia

Abstract: Under study are some commuting rank 2 differential operators with polynomial coefficients. We prove that, for every spectral curve of the form $w^2=z^3+c_2z^2+c_1z+c_0$ with arbitrary coefficients $c_i$, there exist commuting nonselfadjoint operators of orders 4 and 6 with polynomial coefficients of arbitrary degree.

Keywords: commuting differential operators.

Funding Agency Grant Number
Russian Foundation for Basic Research 14-01-00178-а
14-11-00441
The first author was supported by the Russian Foundation for Basic Research (Grant 14-01-00178-a); the second and third authors were supported by the Russian Foundation for Basic Research (Grant 14-11-00441).


DOI: https://doi.org/10.17377/smzh.2016.57.510

Full text: PDF file (256 kB)
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English version:
Siberian Mathematical Journal, 2016, 57:5, 819–823

Bibliographic databases:

Document Type: Article
UDC: 517.957
Received: 20.01.2016

Citation: A. B. Zheglov, A. E. Mironov, B. T. Saparbayeva, “Commuting Krichever–Novikov differential operators with polynomial coefficients”, Sibirsk. Mat. Zh., 57:5 (2016), 1048–1053; Siberian Math. J., 57:5 (2016), 819–823

Citation in format AMSBIB
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\pages 1048--1053
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    This publication is cited in the following articles:
    1. 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
  • Сибирский математический журнал Siberian Mathematical Journal
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