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

Сибирский математический журнал

V. S. Oganesyan¹ 

[1] Moscow State University

关键词: commuting differential operators;   

DOI  :  10.1134/S0037446618010111

学科分类：数学（综合）

来源: Izdatel stvo Instituta Matematiki Rossiiskoi Akademii Nauk

【 摘 要 】

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.

【 授权许可】

CC BY