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Commuting Krichever–Novikov differential operators with polynomial coefficients

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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 2 z 2+c 1 z+c 0 with arbitrary coefficients c i , there exist commuting nonselfadjoint operators of orders 4 and 6 with polynomial coefficients of arbitrary degree.

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Authors and Affiliations

  1. Moscow State University, Moscow, Russia

    A. B. Zheglov

  2. Sobolev Institute of Mathematics Novosibirsk State University, Novosibirsk, Russia

    A. E. Mironov & B. T. Saparbayeva

Authors
  1. A. B. Zheglov
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  2. A. E. Mironov
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  3. B. T. Saparbayeva
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Corresponding author

Correspondence to A. B. Zheglov.

Additional information

Dedicated to A. P. Veselov on the occasion of his 60th birthday.

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).

Moscow; Novosibirsk. Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 57, No. 5, pp. 1048–1053, September–October, 2016; DOI: 10.17377/smzh.2016.57.510.

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Zheglov, A.B., Mironov, A.E. & Saparbayeva, B.T. Commuting Krichever–Novikov differential operators with polynomial coefficients. Sib Math J 57, 819–823 (2016). https://doi.org/10.1134/S0037446616050104

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  • DOI: https://doi.org/10.1134/S0037446616050104

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