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Siberian Mathematical Journal

, Volume 59, Issue 1, pp 102–106 | Cite as

Alternative Proof of Mironov’s Results on Commuting Self-Adjoint Operators of Rank 2

  • V. S. OganesyanEmail author
Article
  • 19 Downloads

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 

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Copyright information

© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  1. 1.Moscow State UniversityMoscowRussia

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