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Commuting matrix differential operators of arbitrary rank. (English. Russian original) Zbl 0598.47049
Sov. Math., Dokl. 30, 515-518 (1984); translation from Dokl. Akad. Nauk SSSR 278, 1048-1052 (1984).
In this note we solve the problem of the classification of commuting pairs of ordinary linear differential operators in general position with matrix coefficients. We put into correspondence with each such pair its ”spectral data”, a collection of nonsingular curves, holomorphic bundles over them, Tyurin parameters, and certain gluing parameters at points of intersection of the curves. The ”spectral data” are independent, and the operators are defined completely.

MSC:
47E05 General theory of ordinary differential operators (should also be assigned at least one other classification number in Section 47-XX)
34A30 Linear ordinary differential equations and systems, general
34L99 Ordinary differential operators
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