Alternative Proof of Mironov’s Results on Commuting Self-Adjoint Operators of Rank 2
- Authors: Oganesyan V.S.1
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Affiliations:
- Moscow State University
- Issue: Vol 59, No 1 (2018)
- Pages: 102-106
- Section: Article
- URL: https://journals.rcsi.science/0037-4466/article/view/171673
- DOI: https://doi.org/10.1134/S0037446618010111
- ID: 171673
Cite item
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.
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About the authors
V. S. Oganesyan
Moscow State University
Author for correspondence.
Email: vardan.o@mail.ru
Russian Federation, Moscow